Download Data Analysis 9–1 Central Tendencies 9–2 Stem and Leaf Plots 9–3

Unit 9 – Data Analysis
9–1 Central Tendencies
9–2 Stem and Leaf Plots
9–3 Box and Whisker Plots
9–4 Graphs: Bar, Line, Circle
9–5
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Probability
Section 9-1: Central Tendencies (Day 1)
Review Question
What is factoring? Breaking down polynomials
Discussion
If you wanted to know if a company was good to work for, would you want to know the mean, median, or
mode of all of the salaries of the workers? Why? Any one of those statistics could be misleading.
These values are called measures of central tendencies because they describe the middle of the data set.
SWBAT define data
SWBAT calculate the mean, median, mode, and range of a data set
Definitions
Data – pieces of information
Example: My siblings’ ages: 8, 9, 12, 15, 16, 18, 20
Each of those numbers is considered to be data.
The group of numbers is a data set.
Mean – average; add up the numbers then divide by the total amount of numbers
Median – middle number when the data set is in order
Mode – appears most often; can be more than one mode
Range – difference between the biggest and smallest number
Example 1: The age of children in a family: 8, 9, 12, 15, 16, 18, 20. Find the mean, median, mode,
and range.
Mean: 14
Median: 15
Mode: None
Range: 12
Example 2: My cousins ages are: 8, 12, 8, 17, 14, 18, 20, 32. Find the mean, median, mode, and
range.
Mean: 16.1
Median: 15.5
* Notice the difference in finding the median when the data set has an even amount of numbers
Mode: 8
Range: 24
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Example 3: Make up a data set with 7 numbers that has the following characteristics:
Mean: 8 Median: 6 Mode: 2 Range: 25
(2, 2, 4, 6, 7, 8, 27)
Can you come up with another data set that would work?
You Try!
Find the mean, median, mode, and range. Then write a sentence that describes what the data set could
represent.
1. 4, 7, 9, 12, 2, 8, 7 mean - 7, median - 7, mode - 7, range - 10
2. 70, 88, 85, 78, 88, 70 mean - 79.8, median - 81.5, mode - 88 & 70, range - 18
3. Make up a data set with 6 numbers that has the following characteristics:
Mean: 6 Median: 5 Mode: 1 Range: 13 1, 1, 4, 6, 10, 14
What did we learn today?
Section 9-1 Homework (Day 1)
1. Write down a guess for the mean. Then calculate the exact value of the mean.
a. 1, 2, 3, 4, 5, 6, 7
Guess:
Actual:
b. 20, 40, 60, 100, 150
Guess:
Actual:
c. 1, 3, 5, 7, 9, 11
Guess:
Actual:
d. 2, 10, 25, 30, 40, 10000
Guess:
Actual:
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2. Find the mean, median, mode, and range for each of the following data sets. Then write a sentence
that describes what the data set could represent.
a. 41, 37, 43, 43, 36
b. 2, 8, 16, 21, 3, 8, 9, 7, 6
c. 14, 6, 8, 10, 9, 5, 7, 13
d. 7.5, 7.1, 7.4, 7.6, 7.4, 9.0, 7.9, 7.1
3. Make up a data set with 7 numbers that has the following characteristics:
Mean: 10, Median: 8, Mode: 4, Range: 22.
4. Make up a data set with 6 numbers that has the following characteristics:
Mean: 5, Median: 3, Mode: 1, Range: 16.
5. Consider the following data set: 2, 8, __. If the mean of the data set is 10, explain why the ___ has to
contain a number greater than 10.
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Section 9-1: Central Tendencies (Day 2)
Review Question
How do you find the median of a data set with an even amount of numbers? Find middle two numbers;
then take the mean
Discussion
Yesterday, we defined and calculated the mean, median, and mode of data sets. These values are called
measures of central tendencies. They are called this because they describe the middle of a data set.
Today, we are going to try to figure out which one best describes a data set. Consider a data set of the
amount of points Lebron James scores in a game: 16, 18, 19, 19, 46, 48, 50.
How does the NBA summarize this data set? Mean
Why don’t they use the median? Could be misleading
Today, we want to figure out the best way to summarize any data set.
SWBAT identify the correct measure of central tendency to use
SWBAT identify the effect of an outlier on the mean and median
Definitions
measures of central tendencies – values that describe the middle of a data set
Example 1: Company A’s mean salary is $55,000. Company B’s mean salary is $224,000.
Which company do you want to work for?
Is it possible to work for company B and make less money than for company A? How? Company B
could have a person that makes a lot more than the rest of the employees.
Be aware of how statistics can be misleading!
Company A’s Salaries
40,000
45,000
50,000
60,000
80,000
Company B’s Salaries
30,000
30,000
30,000
30,000
1,000,000
What is the mean salary of each company? $55,000 and $224,000
What is causing the distortion in the mean? Outlier
Outlier – an extreme data value
How does this outlier affect the mean? Greatly; show the results: 30,000 → 224,000
How does this outlier affect the median? Minimally: show the results: 30,000 → 30,000
What measure of central tendency best describes the salaries of each company? Why?
Use the mean for Company A and the median for Company B.
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How do you know when to use the mean or the median?
*Use the mean when the data is “close together.”
*Use the median when you have outliers.
Discuss “close together”. If talking about test scores 30 points isn’t close together. If talking about
distance traveled 30 miles might be close together.
Example 2: Which measure of central tendency best summarizes each of the following data sets?
a. 10, 12, 14, 15, 1000 (money in people’s pockets) median
b. 3.5, 3.2, 3.6, 3.6, 3.2 (grade point averages) mean
c. 94 99 95 60 92 65 93 98 61 (test scores) median
Example 3: An article in the newspaper stated that teachers are overpaid. It stated that the average
teacher salary was $61,000.
How could that statistic be misleading? Discuss how teachers with longer tenures make more money
than newer teachers
What would be a better statistic to use? Why? Median b/c a few teachers that make $90,000 raise the
average greatly
You Try!
Find the mean, median, mode, and range. Then select which measure of central tendency best
summarizes each of the following data sets.
1. 14, 18, 22, 28, 30, 35 mean: 24.5, median: 25, mode: none, range: 21; MEAN (close together)
2. 2, 4, 6, 8, 10, 12, 250 mean: 41.7, median: 8, mode: none, ragne: 248; MEDIAN (outlier)
What did we learn today?
Section 9-1 Homework (Day 2)
1. Find the mean, median, mode, and range for each of the following data sets. Then state whether
the mean or median would best describe the data set.
a. 1, 2, 2, 4, 5, 6, 7, 100
b. 85, 86, 87, 96, 96, 97, 98
2. Make up a data set with 7 numbers that would be best described by the median.
3. Make up a data set with 7 numbers that would be best described by the mean.
4. What effect does a large number have on a data set’s mean?
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5. What effect does a large number have on a data set’s median?
6. A shoe store collected data on all of the sizes of shoes that customers bought. The manager is going to
use this data to place his next order. He is trying to figure out what size to buy the most of. What
measure of central tendency should he use? Why?
7. Most professional basketball players make between $2,000,000 and $5,000,000. A few players make
over $20,000,000. (Write answers in complete sentences)
a. The owner of a team was trying to show that athletes make a large amount of money. What statistic
did he use? Why?
b. The players were trying to show that they did not make enough money. What statistic did they use?
Why?
c. What statistic best summarizes the player’s salaries? Why?
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Section 9-1: Central Tendencies (Day 3)
Review Question
Find the mean and median of each data set.
1. 1, 2, 3, 4, 5 Mean: 3, Median: 3
2. 1, 2, 3, 4, 5, 100000 Mean: 16669, Median: 3.5
What effect does an outlier have on a data set’s mean? Great
What effect does an outlier have on a data set’s median? Minimal
Discussion
Why is it important to know the effects of an outlier? People use statistics to mislead us
Can someone give me an example where this could be used to someone’s advantage? Salaries at
companies
SWBAT identify the correct measure of central tendency to use
SWBAT identify the effect of an outlier on the mean and median
You will work together to come up with thorough solutions to the following questions. The solutions will
include calculation and sentences. You must work together in order to be successful. The ability to work
with others is one of the most desirable skills that employers want. You will have to learn how to get
along with people at work that you do not like. Today is a good time to practice this skill.
What did we learn today?
Section 9-1: In-Class Assignment (Day 3)
1. In your own words, define each of the following terms. Then describe how to find each of them
including special cases.
Mean –
Median –
Mode –
Range –
2. Find the mean, median, mode, and range for each data set. Then write a sentence that describes what
measure of central tendency best describes the data set.
a. 1, 2, 3, 3, 40
b. 20, 22, 24, 26, 50, 52, 56, 56
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c. 44, 44, 44, 46, 47, 48, 180
d. 180, 190, 140, 150, 160, 170,
3. Give a real life example (shoe store, players’ salaries) where the mean would be the most applicable.
Give a reason why the mean would be the best measure of central tendency.
4. Give a real life example (shoe store, players’ salaries) where the median would be the most
applicable. Give a reason why the median would be the best measure of central tendency.
5. Give a real life example (shoe store, players’ salaries) where the mode would be the most applicable.
Give a reason why the mode would be the best measure of central tendency.
6. All of the houses in your neighborhood are between $100,000 and $125,000. A family moves in and
builds a $750,000 house.
a) How would this affect the median value? Why?
b) How would this affect the mean value? Why?
7. The following data represents the amount of Girl Scout cookies each member of your troop sold: 1, 2,
3, 4, 5, 80, 120, 205, 225.
a) What measure of central tendency would you use to make your troop look good? Why?
b) What measure of central tendency would you use to make the troop look bad? Why?
8. Four of the starters on your basketball team are 5’7”. The fifth starter is Yao Ming (7’7”).
a) What measure of central tendency best describes the height of your team? Why?
b) What measure of central tendency would make your opponents believe that your team is tall?
9. Can the average of a data set be bigger than the highest number in the data set? Why or why not?
(write answer by giving an example and using complete sentences)
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Section 9-2: Stem-and-Leaf Plots (Day 1)
Review Question
When should you use the mean to summarize a data set? When the numbers are close together
When should you use the median to summarize a data set? When there is an outlier
Discussion
Yesterday, we summarized data sets by using the mean, median, and mode of data sets. Today, we are
going to start summarizing data sets by graphing them.
The class average on the last test was 84%. Why doesn’t this statistic tell us the entire story?
What else would you like to know about the data set? Each test result, highest/lowest score,
distribution
SWBAT construct a stem-and-leaf plot given a data set
SWBAT read and apply information about a given stem-and-leaf plot
Definition
Stem-and-leaf plot - shows how often data values occur and how the data set is distributed
What does distributed mean?
Example A: 1, 2, 3, 4, 5
Example B: 1, 100, 1000, 5000
Example C: 1, 2, 3, 4, 5, 60
How would you describe the distribution in Example A? Close together
How would you describe the distribution in Example B? Far apart
How would you describe the distribution in Example C? Close together with an outlier
There are three ways (close together, far apart, close together with an outlier) that we will describe
the distribution of data sets.
Example 1: Reading a stem and leaf plot:
Math class’ test scores.
Stems
Leaves
6
0 9 9
7
1 3 5 6 7 8 9
8
0 2 3 7 8 9 9 9
9
0 1 2 3 5 7
Key: 7|1 = 71
1. What is the lowest score? 60
2. What is the greatest score? 97
3. How many numbers over 87? 10
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4. Find the mode of the data. 89
5. Find the median of the data. 83
6. Find the mean of the data. 82.3
Example 2: Making a stem and leaf plot:
Points Kobe Bryant scored in the last 18 games:
38, 46, 39, 42, 20, 55, 20, 37, 52, 30, 49, 27, 35, 31, 34, 23, 34, 20
Stems
Leaves
2
0 0 0 3 7
3
0 1 4 4 5 7 8 9
4
2 6 9
5
2 5
Key: 5 | 2 = 52
Example 3: Making a stem and leaf plot:
The different weights of boys on the wrestling team:
118, 166, 139, 185, 144, 164, 121, 137, 142, 147, 127, 137, 131, 134, 169, 147, 155, 160
Stems
Leaves
11
8
12
1 7
13
1 4 7 7 9
14
2 4 7 7
15
5
16
0 4 6 9
17
18
5
Key: 11|8 = 118
You Try!
For each problem, draw a stem and leaf plot, find the mean, median, mode, and range.
Does the mean or median best describe the data set?
Describe the distribution of the data set.
1. 10, 10, 12, 18, 22, 24, 41 mean- 19.57, median- 18 (either), mode- 10, range- 31, Close
2. 113, 114, 121, 132, 162, 360 mean- 167, median- 126.5, mode- none, range- 247, Close w/ outlier
What did we learn today?
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Section 9-2 Homework (Day 1)
1. Make a stem-and-leaf plot for each set of data.
a. 23, 36, 24, 13, 24, 25, 32, 33, 17, 26, 24
b.
347, 334, 346, 330, 348, 347, 359, 344
2. Use the stem-and-leaf plot at the right that shows
the number of hours per week certain students worked.
1
2
3
a. How many students are represented on the stem-and-leaf plot?
b. Find the median of the data.
1 1 4 5
0 5 6
1 8 8 9
Key 2 0 = 20
c. Find the mode of the data.
3. Determine the mean, median, mode, and range of the data shown in each stem-and-leaf plot.
a.
0
1
2
1 2 2 3
3 4 5 5
0 0 0 1 3
b.
Key 2 0 = 20
2
3
4
0 0 0 2 3 5 7
1 2
0
Key 4 0 = 40
mean =
median =
mean =
median =
mode =
range =
mode =
range =
c.
22
23
24
d.
1 1 2 7
3 3 9
0 6 8
Key 24 0 = 240
0
1
2
1 3 3 4 7
2 2 24 5 6
0 0 0 1
Key 2 0 = 20
mean =
median =
mean =
median =
mode =
range =
mode =
range =
4. Describe the distribution of each data set.
a. 10, 12, 14, 16, 18, 20, 25, 28
b. 10, 50, 110, 180, 240, 650
c. 2, 5, 8, 12, 15, 18, 97
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Section 9-2: Stem-and-Leaf Plots (Day 2)
Review Question
What does a stem and leaf plot show us about a data set? Each data point; distribution
What does distributed mean? How close/spread out the data is
Discussion
Sometimes you need to compare two different data sets. An easy way to do this is by graphing both sets
of data in one picture. For example, if you are trying to decide between two stocks to buy. You could
graph the prices of both stocks during the past six months on a graph. Then you could compare the
results. What stock would you buy? Why?
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25
20
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SWBAT construct a back to back stem and leaf plot given two sets of data
SWBAT compare two different sets of data
Example 1: Test Scores
Class A: 79, 81, 81, 82, 83, 83, 85, 85, 85, 90, 91, 91
Class B: 62, 65, 68, 69, 90, 91, 92, 92, 94, 96, 96, 97, 98
a. Based on the data sets, which class did better? Why? Depends on what you think is better
b. Construct a back to back stem and leaf plot.
6 2 5 8 9
9 7
5 5 5 3 3 2 1 1 8
1 1 0 9 0 1 2 2 4 6 6 7 8
Key 9 0 = 90
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c. Based on the plot, which class did better? Why? Depends on what you think is better
d. What can you say about the distribution of the grades for each class? Class A: even; Class B: spread
e. Calculate the mean and median for each class.
Class A
Class B
Mean: 84.6
Mean: 85.4
Median: 84
Median: 92
f. Based on the statistics which class did better? Why? Class B; higher mean and median
g. Which statistic is more appropriate for each class? Why?
Either for Class A. Mean for Class B.
What did we learn today?
Section 9-2 In-Class Activity (Day 2)
1. Collect data: Measure the height of all students in inches. Then enter data in table.
Boy or Girl
Height (inches)
Boy or Girl
Height (inches)
2. Construct a back to back stem and leaf plot.
3. Calculate the mean and median for the boys and girls, separately.
4. Is the mean or median more appropriate for the boys? girls? Why?
5. Based on the graph and statistics, who is taller? Why?
6. Write one sentence to summarize the boys’ heights. Then write one sentence to summarize the girls’
heights.
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Section 9-2 Homework (Day 2)
1. Company A salaries (in thousands): 26, 28, 32, 36, 36, 36, 37, 98, 98, 99
Company B salaries (in thousands): 45, 48, 48, 55, 56, 58, 60, 61, 70, 70
a. Make a back to back stem and leaf plot for the data sets. (including key)
b. Based on the plot, which company do you want to work for? Why?
c. Find the mean, median, and mode for each company’s salaries.
d. What statistic best summarizes each company’s salaries? Why?
e. Based on the statistics, which company do you want to work for? Why?
2. Give an example of a data set with seven numbers in it with the following characteristics:
a. The median is less than the mean.
b. The median is greater than the mean.
c. The median is equal to the mean.
3. Give an example of a data set that would only have one stem.
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Section 9-3: Box-and-Whisker Plots (Day 1)
Review Question
What does a back to back stem and leaf plot show us? Allows us to compare two different data sets
Discussion
1, 2, 3, 50, 52, 206, 211
72, 73, 74, 75, 76, 77, 78
What is the mean of these two data sets? 75
What is different about these two data sets? Distribution
What does distribution mean? How close/spread out the data is
Notice the first data set has groups of numbers that are close together. But overall the data is spread out.
Today, we will use a graph that can show this.
SWBAT construct a box and whisker plot given a set of data
SWBAT read a box and whisker plot
Definitions
Box and Whisker plot - plot that uses five different values to display distribution of a data set
Five critical points in a box and whisker plot:
Lower Extreme – smallest number
Upper Extreme – greatest number
Median – middle number
Lower Quartile – median of the lower half
Upper Quartile – median of the upper half
LE
LQ
Median
UQ
UE
Example 1: Making a box and whisker plot:
2, 3, 4, 5, 6, 7, 8
LE: 2 LQ: 3
Median: 5
UQ: 7
UE: 8
Example 2: Making a box and whisker plot
12, 8, 6, 8, 2, 20, 16, 10
Rewrite the data set in order: 2, 6, 8, 8, 10, 12, 16, 20
*Be careful when dealing with a data set that has an even amount of pieces.
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LE: 2 LQ: 7
Median: 9
UQ: 14
UE: 20
Example 3: Reading a box and whisker plot
2
3
4
5
6
7
8
9
10
11
12
Find the following values.
Lower Extreme: 2, Upper Extreme: 4, Median: 7, Lower Quartile: 10, Upper Quartile: 12
You Try!
Find the mean, median, mode, and range. Draw a stem and leaf plot. Draw a box and whisker plot.
1. 10, 12, 19, 20, 28, 34, 36, 42, 48
Mean-23.7, Median-28, Mode-None, Range-38
LE: 10, LQ: 15.5, Med: 28, UQ: 39, UE: 48
2. 35, 36, 44, 46, 50, 56, 58, 67, 71, 72 Mean-53.5, Median-53, Mode-None, Range-37
LE: 35 LQ: 44 Med: 53, UQ: 67, UE: 72
What did we learn today?
Section 9-3 Homework (Day 1)
For each data set find each of the following:
a. Find the mean, median, mode, and range (Circle which one best summarizes the data set)
b. Draw a stem and leaf plot
c. Draw a box and whisker plot. (Describe the distribution of the data set.)
1. 2, 4, 6, 8, 10, 12, 60
2. 100, 140, 120, 115, 180, 185, 120, 100
3. 80, 60, 90, 92, 86, 100, 45, 45, 90
4. 10, 12, 14, 18, 20, 30, 32, 100, 120, 120
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Section 9-3: Box-and-Whisker Plots (Day 2)
Review Question
What does a box and whisker plot show us? Distribution
What are the five critical points in a box and whisker plot? lower extreme, lower quartile, median,
upper quartile, upper extreme
Discussion
The median breaks a data set in half. What do the lower and upper quartiles do? Breaks the data set
into quarters
25%
25%
25%
25%
25%
What percent of the data is represented by the ‘box’ portion of the graph? 50%
This value is called the Interquartile Range (IQR). It is the upper quartile minus the lower quartile.
SWBAT construct a box and whisker plot given a set of data
SWBAT read the quartiles of a box and whisker plot
Example 1: 2, 8, 12, 18, 20, 30, 32, 40
Find the five critical values. Then draw a box and whisker plot.
LE: 2 LQ: 10 Median: 19
UQ: 31 UE: 40
What percent of the data is greater than 19? 50%
What percent of the data is less than 31? 25%
What percent of the data is less than 10? 25%
What percent of the data is between 2 and 31? 75%
What is the IQR? 21
You Try!
1. For the following data set: 10, 14, 18, 22, 34, 34, 44
Find the mean, median, mode, and range. Mean-25.1, Median-22, Mode-None, Range-34
Draw a stem and leaf plot.
Draw a box and whisker plot. LE: 10, LQ: 14, Median: 22, UQ: 34, UE: 44
What percent of the data is below 34? 25%
What percent of the data is above 22? 50%
What is the IQR? 20
2. For the following data set: 15, 26, 42, 48, 50, 66, 76, 82
Find the mean, median, mode, and range. Mean-50.6, Median-49, Mode-None, Range-67
Draw a stem and leaf plot.
Draw a box and whisker plot. LE: 15, LQ: 34, Median: 49, UQ: 71, UE: 82
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What percent of the data is below 49? 50%
What percent of the data is in between 34 and 82? 75%
What is the IQR? 37
What did we learn today?
Section 9-3 Homework (Day 2)
1. Given the following data set: 24, 10, 18, 36, 8, 64, 22, 46, 60, 54, 65, 10
a. Find the mean, median, mode, and range.
b. Draw a stem and leaf plot.
c. Draw a box and whisker plot. List the five critical points
2. Answer the following questions based on the above box and whisker plot.
a. What % of the data is above 57?
b. What % of the data is above 30?
c. What % of the data is above 14?
d. What % of the data is below 14?
e. What % of the data is between 14 and 57?
f. What is the IQR?
3. If you add one large number to a data set, how would the number affect the lower quartile, median,
and upper quartile? Why?
4. A 35 year-old man goes to the hospital to get a cancerous tumor removed. He asks the nurse,
“Normally, how old are the men who come in here for this procedure?” She responds, “We get men of all
ages. We get five year-olds all the way up to 85 year-olds. But you would be about normal.” Based on
the nurse’s response, estimate the mean, median, mode, lower extreme, and upper extreme.
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Section 9-3: Box-and-Whisker Plots (Day 3)
Review Question
What percent of the data is above the median? 50%
How do you calculate the IQR? UQ minus LQ
Discussion
Can you draw a box and whisker plot that shows a data set where the data is close together in the
beginning but spread out in the end?
SWBAT describe a data set given a box and whisker plot
Example 1:
1. What can be concluded about the data set from this box-and-whisker plot?
The data in the lower half is close together.
The data in the upper half is further apart.
2. Make up a data set that could be represented by this box-and-whisker plot:
(1, 4, 6, 8, 10, 15, 35, 45, 75)
3. Why couldn’t the data set be 1, 2, 3, 4, 5, 6, 7? The plot doesn’t show an even distribution
Example 2:
5
10
15
20
25
1. What percent of the data is above 15? 50%
2. What percent of the data is below 20? 75%
3. What can be concluded about the data set from this box-and-whisker plot? The data is evenly
distributed.
4. Make up a data set that could be represented by this box-and-whisker plot.
(5, 7, 10, 12, 13, 15, 17, 19, 20, 21, 22, 25)
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Example 3: Grades
Class A
Class B
60
70
80
90
1. Write a sentence to summarize Class A’s grades. 75% scored above a ‘C’; half the class scored a
‘B’
2. Write a sentence to summarize Class B’s grades. 75% scored above a ‘B’; 50% scored a ‘B’
3. Which class did better? Why? Class B; 75% scored above a ‘B’; 50% scored a ‘B’
You Try!
Draw a box-and-whisker plot that has 75% of the data greater than 19 and 25% of the data above 41. The
data set has a lower extreme of 14, upper extreme of 55, and a median of 35.
What did we learn today?
Section 9-3 In-Class Assignment (Day 3)
1.
a. Write one sentence that summarizes the box and whisker plot.
b. Make up a data set that could be represented by this box-and-whisker plot.
2. Refer to the box-and-whisker plots below that represent two basketball teams’ scores for a season.
Team A
Team B
40
50
60
70
80
90
100
a. Write one sentence to summarize the first team’s season scores.
b. Write one sentence to summarize the second team’s season scores.
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c. Which team scored more points? How do you know?
3. Given the data set: 2, 3, 4, 5, 8, 15, 30, 50, 100, how do you know the following plot is wrong?
4. Draw a box-and-whisker plot in which 50% of the data is below 24 and 75% of the data is below 38.
5. Given the following data set: 10, 12, 20, 22, 24, 32, 45, 55, 61, 68
a. Find the mean, median, mode, and range.
b. Draw a stem and leaf plot.
c. Draw a box and whisker plot. List the five critical points
d. Answer the following questions based on the above box and whisker plot.
i. What % of the data is above 28?
ii. What % of the data is above 20?
iii. What % of the data is above 68?
iv. What % of the data is below 20?
v. What % of the data is between 20 and 68?
vi. What is the IQR?
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Section 9–4: Graphs: Bar, Line, Circle (Day 1)
Review Question
What are the different ways that we have been summarizing data?
Mean, Median, Mode, Range; Stem/Leaf; Box/Whisker
Discussion
What type of graph would you use to show the number of wins each team in the Steeler’s division had?
Why wouldn’t a stem/leaf plot be good? Only shows one data set
Why wouldn’t a box/whisker plot be good? Only shows one data set
SWBAT read a bar graph
SWBAT construct a bar graph
Definition
Bar graph – displays quantities of data that have been organized into categories
Example 1: Reading a bar graph.
School District
1. Which school district has the greatest enrollment? Penn Hills
2. Which school district has the least enrollment? Brentwood
3. How many students are in the Bethel Park School District? 5000
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Brentwood
Bethel Park
Gateway
Penn Hills
Mt. Lebanon
7000
6000
5000
4000
3000
2000
1000
0
Carlynton
Number of Students Enrolled
Student Enrollment
Example 2: Reading a double bar graph.
Number
Boys vs. Girls in Math Classes
20
18
16
14
12
10
8
6
4
2
0
Girls
Boys
Period 1
Period 5
Period 8
Class Periods
1. How many students are in each class period? Period 1: 30, Period 5: 29, Period 8: 29
2. What percent of Period 1 is boys? 53%
3. What percent of Period 5 is girls? 34%
Example 3: Making a bar graph.
Sports
Football
Basketball
Soccer
Tennis
Baseball
Number of
Students
56
34
29
16
22
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You Try!
1. Students were surveyed about their favorite color. The results are as follows:
Blue: 26, Green: 12, Pink: 8 Yellow: 4, Red: 18.
Make a bar graph of the results.
What did we learn today?
Section 9–4 Homework (Day 1)
1. Students were surveyed about their favorite sport. The table below displays the results.
Sport
Football
Basketball
Baseball
Hockey
Golf
Number of
Students
45
65
38
32
20
a. Draw a bar graph of the data.
b. How many students were surveyed?
c. How many more students chose basketball than hockey?
d. What percent of the students chose each sport?
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2. The double bar graph below shows the amount of money spent weekly on food.
Number of Responses
Amount Spent Weekly on Food
12
10
8
Males
6
Females
4
2
0
0-24
5
25-49
10
50-74
15
75-99
20
10025
124
12530
149
15035
174
Dollars
a. How many males were surveyed?
b. How many females were surveyed?
c. What percent of people surveyed were males?
d. What percent of people that spent $5 were females?
3. Does there appear to be a relationship between gender and amount of money spent weekly on food?
Explain thoroughly.
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Section 9–4: Graphs: Bar, Line, Circle (Day 2)
Review Question
When is it appropriate to use a bar graph?
When you have different categories of data.
Discussion
Could you use a bar graph to show a teacher’s salary over each year of her career? Yes.
Is it the best graph to use? It would be tedious to draw thirty different bars. It would be easier to
draw a point.
SWBAT read a line graph
SWBAT construct a line graph
Definition
Line graph – displays two sets of data that is connected in some way; usually data changing over time
Example 1: Reading a line graph.
1. What day has the highest temperature? Friday
2. What is the lowest temperature? 15°
3. What is the mean temperature? 22°
Temperature
40
30
20
Temperature
10
0
M
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T
W
Th
F
Example 2: Making a line graph.
Year
Population
(thousands)
1970
56
1980
60
1990
66
2000
68
2010
80
You Try!
1. Make a line graph.
Year
Salary
(thousands)
2000
56
2002
60
2004
90
2006
93
2008
94
What did we learn today?
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Section 9–4 Homework (Day 2)
1. What day has the highest amount of pushups?
2. What day has the lowest amount of pushups?
3. What is the mean for the amount of pushups?
4. What is the median for the amount of pushups?
5. What is a good prediction for the amount of pushups that will be done on Sunday?
6. Make a line graph.
Year
Value of Car
(Thousands)
2007
24
2008
20
2009
18
2010
15
2011
11
7. How much will the car be worth in 2014?
8. What is different about a line graph and a bar graph?
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Section 9–4: Graphs: Bar, Line, Circle (Day 3)
Review Question
How do you change a fraction to a percent? Divide, move decimal two place to the right
Discussion
What is a circle graph? Uses percentages
What do the percents add up to? 100%
You should like circle graphs because you understand percents. For example, you understand a 92% on a
quiz better than a 49/53 on a quiz.
SWBAT create a circle graph given a set of data
Definition
circle graph – displays data as percentages
Example 1: Using your number sense to draw a circle graph. The goal is for the students to use their
number sense to estimate each piece. Show students how to estimate percents on the circle graph by
using 50% and 25% to guide them.
Listed below are the results to a survey of students on what their favorite color is:
10% Green, 54% Blue, 22% Pink, and 14% Red.
Make a circle graph based on these results.
What color should we put in the graph first? Why? Blue, it’s easy to estimate 54%.
What color should we put in next? Why? Pink, it’s easy to estimate 22%.
Finally, notice that green and red add up to about 25%.
Example 2: Have the students make a pie chart for the following data:
12% ‘A’s’, 13% ‘B’s’, 30% ‘C’s’, and 45% ‘D’s’.
Notice that the A’s and B’s add up to 25% and the C’s and D’s add up to 75%. The students should
estimate using these values.
Example 3: Making a circle graph.
Students in 8th grade were asked to choose their favorite subject. The results are 48 English, 30 Math, 28
Science, 36 History, and 58 Gym.
What do we need to make a circle graph? Percents
English – 48/200 = .24 = 24%
Math – 30/200 = .15 = 15%
Science – 28/200 = .14 = 14%
History – 36/200 = .18 = 18%
Gym – 58/200 = .29 = 29%
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Draw the pie chart together. Show students how to estimate percents on the pie chart by using 50% and
25% to guide them.
Discussion
When someone is presenting information in a graph they can sometimes trick you. For example, the
government ONLY spent 5% on salaries. That does not sound like a lot. This would not look like a lot in
a circle graph either. But if the total budget was $200 billion, then 5% represents a large amount. In
summary, small pieces of a pie graph could represent a large amount. Think about a pizza the size of
your school. If you only had a 5% piece, it would still be a huge piece of pizza.
What did we learn today?
Section 9–4 In-Class Assignment (Day 3)
1. 130 students were surveyed about their favorite sport. The results are shown in the circle graph below.
Favorite Sports
a. Which sport was most popular?
b. Which sport was least popular?
Hockey
15%
c. What percent of the students chose hockey or baseball as
their favorite?
Golf
8%
Football
31%
Baseball
19%
Basketball
27%
d. What percent of the students chose football or golf as their favorite?
e. What percent of the students did not choose basketball as their favorite?
2. You make $1800 per month. Your monthly expenses are shown below.
Mortgage - $756 Entertainment - $180
Transportation - $468 Utilities - $396
a. Calculate what percent of money is spent on each expense.
b. Make a circle graph based on the percentages above.
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c. Make a bar graph based on the monthly expenses.
3. What could influence how much money you spend on each of the following?
a. Utilities –
b. Transportation –
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Section 9–4: Graphs: Bar, Line, Circle (Day 4)
Review Question
What type of data set is best suited for a circle graph? Percents
What do the percents have to add up to? 100%
Discussion
How do we calculate percents to create a circle graph? Divide
How do you think we would extract information from a circle graph? Multiply
SWBAT extract information from a circle graph
Example 1: 120 students were surveyed about their favorite sport. The results are shown in the pie chart
below.
Favorite Sports
Hockey
15%
Golf
8%
Football
31%
Baseball
19%
Basketball
27%
Estimate how many students play each sport using the estimating skills. Talk about what 50% would be.
Half of 120 is 60; then base your estimations from there; Football  40
Calculate how many students chose each sport. Then compare it to your estimation.
Remember, we divide to make a pie chart. We must multiply to extract information from a pie chart.
Football = 120 x 31% = 3720 There is no way that this answer can be correct since only 120 total
students were surveyed. Multiplying by 31% is a common mistake; answer would be unreasonable.
Football = 120 x .31 = 37.2  37
Basketball = 120 x .27 = 32.4  32
Baseball = 120 x .19 = 22.8  23
Hockey = 120 x .15 = 18  18
Golf = 120 x .08 = 9.6  10 Multiplying by .8 is a common mistake.
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What did we learn today?
Section 9–4 In-Class Assignment (Day 4)
1. 150 students were surveyed about their favorite color. The results are shown in the pie chart below.
a. Which color was most popular?
b. Which color was least popular?
c. What percent of the students chose blue or yellow as
their favorite?
2. Calculate how many students chose each color.
Blue =
Yellow =
Purple =
Green =
Red =
3. A car dealership sold a total of 80 cars. They sold 40 Accords, 25 Civics, and 15 Odysseys.
a. What percent of the cars sold were Accords?
b. What percent of the cars sold were Civics?
c. What percent of the cars sold were Odysseys?
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4. The circle graph below shows the Cooper’s family budget. The Cooper family has a total monthly
income of $2,463.
a. How much money did they spend on food?
b. How much money did they spend on transportation?
c. How much money did they spend on clothing and housing?
d. If they doubled their clothing cost, how much money would they spend?
e. If their monthly income was raised to $3250, how much money would they spend on
food?
7. You make $2200 per month. Your monthly expenses are shown below.
Mortgage - $1020
Entertainment - $180
Transportation - $550
a. Calculate what percent of money is spent on each expense.
b. Make a circle graph based on the percentages above.
c. Make a bar graph based on the monthly expenses.
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Utilities - $450
Section 9–4: Graph: Bar, Line, Circle (Day 5)
Review Question
What type of data set is best suited for a circle graph? Percents
Discussion
What are bar graphs? Graph with categories
How are they different from circle graphs? Don’t use percents
Where do you see them? Summarize data
What do they represent? Categories of data
SWBAT read a circle graph and bar graph
SWBAT create a circle graph and bar graph given a set of data
Example 1: Making a Bar Graph
Listed below are student’s favorite colors:
15 Blue
20 Green
25 Yellow
45 Orange
35 Purple
Draw bar graph together. Show students how to pick good starting and ending points for their graph.
Also, discuss proper use of scale. Notice in this example it would be inappropriate to use a scale of 50. A
scale of every 5 or 10 would be appropriate.
*Talk about how statistics can be misleading. If you choose a small or large scale the data could be
interpreted in a different manner.
Example 2: Making a circle graph using the data from example 1.
What do we need to make a circle graph? Percents
Blue – 15/140 = .107 = 10.7% = 11% Previous lesson
Green – 20/140 = .142 = 14.2% = 14%
Have the students calculate the other color’s percents.
Yellow – 25/140 = .178 = 17.8% = 18%
Orange – 45/140 = .321 = 32.1% = 31%
Purple – 35/140 = .250 = 25% = 25%
Make a circle graph based on these results.
What color should we put in the graph first? Why? Purple, it’s easy to estimate 25%.
What color should we put in next? Why? Blue and Green, they add up to 25%
Finally, estimate the last two colors.
When should we use a circle graph? Percents
When should we use a bar graph? Categories of data
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What did we learn today?
Section 9–4 In-Class Assignment (Day 5)
1. Students were surveyed about their favorite sport. The bar graph below displays the results.
a. How many students chose each of the sports?
Favorite Sport
Football =
60
Basketball =
50
Hockey =
Golf =
b. How many students were surveyed?
Number of Students
Baseball =
40
30
20
10
c. How many more students chose basketball than
hockey?
2. What percent of the students chose each sport?
Football =
Basketball =
Baseball =
Hockey =
3. Draw a circle graph to represent the data.
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f
G
ol
ey
oc
k
H
Ba
se
ba
ll
l
et
ba
l
sk
Sport
d. Which sports were chosen more than 30 times?
Golf =
Ba
Fo
o
tb
al
l
0
4. 170 8th graders were surveyed on their favorite type of music. The results are as follows:
Hip Hop – 44%, Country – 15%, Rock – 18%, Pop – 23%. Calculate how many students
chose each type of music.
Hip Hop –
Country –
Rock –
Pop –
5. Students were surveyed about their favorite brand of shoes. The results are as follows:
Jordans: 86, Nike: 48, Adidas: 28, Converse: 4, and Vans: 18. Make a bar graph.
6. a. Make a line graph.
Year
Value of House
(Thousands)
2009
140
2010
146
2011
156
2012
170
2013
180
b. How much will the house be worth in 2014?
8. Give an example of a data set where a circle graph should be used to summarize it.
9. Give an example of a data set where a line graph should be used to summarize it.
10. Give an example of a data set where a bar graph should be used to summarize it.
350
Section 9–5: Probability (Day 1)
Review Question
When should you use a bar graph, line graph, and circle graph?
categories, two sets of data, percents
Discussion
What does probability mean? Chance
Are the chances of the following events good or bad? Why?
1. You will get HW tonight.
2. That you will dunk a basketball today.
3. That you will be out of school by 5:00 PM.
How would you rate each of the previous events from 0 to 1 where 0 represents impossible and 1
represents certainty?
0
Impossible
¼
Unlikely
½
Equal
¾
Likely
1. You will get HW tonight.
2. That you will dunk a basketball today.
3. That you will be out of school by 5:00 PM.
You said that the chance of you getting homework tonight is good.
Why did you say this? You get HW 3/5 nights.
What does the 1st number represent? How many nights you get it.
What does the 2nd number represent? Total nights
SWBAT calculate simple probability
Definition
Probability – chance something will happen
P(event) = what we want to happen (favorable outcomes)
total events
Example 1: Given a six sided die, calculate the probability of each event:
P(3) = 1/6
P(not 5) = 5/6
P(# < 4) = 3/6
P(2 or 5) = 2/6
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1
Certain
Are the chances of each of these events happening good or bad? Why? The ones greater than 1/2 have
a good chance.
Example 2: A bag of marbles contains 4 green, 5 yellow, and 3 blue marbles. Calculate the probability
of each of the following events. Write each probability as a fraction, decimal, and percent.
P(green) = 4/12, .33, 33%
P(blue) = 3/12, .25, 25%
P(purple) = 0/12, 0, 0%
P(green or blue) = 7/12, .58, 58%
Are the chances of each of these events happening good or bad? Why? The ones greater than 1/2 have
a good chance.
You Try!
1. A spinner has the numbers 1 through 12 on it. Numbers 1 – 4 are red, numbers 5 – 12 are yellow. Find
the probability of each event.
a.
b.
c.
d.
e.
f.
P(8) = 1/12
P(red) = 4/12
P(even) = 6/12
P(not 7) = 11/12
P(less than 6) = 5/12
P(8 or 9) = 2/12
What did we learn today?
Section 9-5 Homework (Day 1)
1. If you rolled a six sided die, are your chances of getting a’1’ good or bad? Why?
2. Give an example of event that would have a ½ probability of happening.
3. For each of the following events, rate the probability from 0 to 1 where 0 represents impossible and 1
represents certainty?
a. That you will take a bus to school tomorrow.
b. That it will rain tomorrow.
c. That you will graduate from high school tomorrow.
d. That you will eat pizza tomorrow.
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4. There are 2 red marbles, 4 blue marbles, 7 green marbles, and 5 yellow marbles in a bag. Suppose one
marble is selected at random. Find the probability of each event. Express each probability as a fraction,
decimal, and percent.
a. P(blue) =
b. P(yellow) =
c. P(not green) =
d. P(purple) =
e. P(red or blue) =
f. P(not blue) =
5. A spinner has the numbers 1 through 10 on it. Numbers 1 - 5 are red, numbers 6 - 10 are yellow. Find
the probability of each event. Express each probability as a fraction, decimal, and percent.
a. P(8) =
b. P(red) =
c. P(even) =
d. P(greater than 2) =
e. P(not 7) =
f. P(8 or 9) =
6. Bench press weight: 150, 145, 140, 160, 155, 150, 185
a. Find the mean, median, mode, and range.
b. Draw a stem and leaf plot.
c. Draw a box and whisker plot.
d. Find the IQR.
e. Based on these statistics, write a sentence that describes the data set’s distribution.
7. Write a COMPLETE SOLUTION. Be sure to include all calculations, explanations, and units.
Finally, write a sentence that summarizes your answer. Ritchie rolled a die 12 times. He got the
number 5 four times. Jimmy rolled a die 25 times. He got the number 5 nine times. Who got a higher
percentage of 5’s?
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Section 9-5: Probability (Day 2)
Review Question
How do you calculate probability?
Favorable outcomes/Total Outcomes
Discussion
What does the word compound? More than one thing
In probability, there are two different types of compound events: independent and dependent.
Let’s try to understand the difference between the two.
1. Does your final math grade depend on your grade on your science quiz? No
2. Does your final math grade depend on your grade on your math quiz? Yes
Therefore, your final math grade is dependent on your grade on your math quiz.
Therefore, your final math grade is independent of your grade on your science quiz.
SWBAT calculate the probability of independent and dependent events
Definitions
Independent events – one event doesn’t affect the outcome of the other
Ex: Tossing a coin and rolling a die
Can someone give me another example of independent events?
Dependent events – one event does affect the outcome of the other
Ex: Picking out a queen (not replacing it) then picking out a king from a deck of cards
Why would this be dependent? Because you are not replacing the first card
Can someone give me another example of dependent events?
Example 1: What is the probability of rolling a six then flipping heads on a coin?
Are the events independent? Yes, 1/6 x 1/2 = 1/12
Example 2: What is the probability of picking a queen (not replacing it) then an ace from a deck of
cards? Are the events independent? No, 4/52 x 4/51 = 16/2652
You Try!
Consider a bag of marbles with 3 blue, 2 green, and 5 yellow. State whether each problem is dependent
or independent. Assume that you will not replace the 1st marble. Then find the probability.
1. P(Green and Yellow) = 2/10 x 5/9 = 10/90
2. P(Green and Blue) = 2/10 x 3/9 = 6/90
3. P(Green and Rolling a 2) = 2/10 x 1/6 = 2/60
4. P(Blue and Rolling an even number) = 3/10 x 3/6 = 9/60
What did we learn today?
354
Section 9-5 Homework (Day 2)
1. Give an example of independent events.
2. Give an example of dependent events.
3. Consider rolling a die and flipping a coin. Are these events dependent or independent?
4. Find the following probabilities based on rolling a die and flipping a coin.
a. P(2 and Heads) =
b. P(Even and Heads) =
c. P(# > 4 and Tails) =
d. P(Heads and Heads) =
5. Consider picking two marbles (without replacing them) from a bag of marbles containing 3 blue, 4
green, and 2 yellow. Are these events dependent or independent?
6. Find the following probabilities based on the bag of marbles in the previous problem.
a. P(Blue and Green) =
b. P(Blue and Yellow) =
c. P(Blue and Blue) =
d. P(Not Blue and Blue) =
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Section 9-5: Probability (Day 3)
Review Question
What is the difference between dependent and independent events?
Independent events – one event doesn’t affect the outcome of the other
Dependent events – one event does affect the outcome of the other
Discussion
How do you calculate the probability of compound events?
Multiply the probability of each event
Let’s take today to practice some of our skills.
SWBAT calculate the probability of independent and dependent events
Example 1: What is the probability of rolling a two then then spinning a two on a ten number spinner?
Are the events independent? Yes; 1/6 x 1/10 = 1/60
Example 2: What is the probability of picking a four of clubs (without replacing it) then a ten from a
deck of cards? Are the events independent? No; 1/52 x 4/51 = 4/2652
What did we learn today?
Section 9-5 In-Class Assignment (Day 3)
1. Explain the difference between dependent and independent events.
2. Explain what is different about calculating the probability of dependent events.
3. Consider rolling a die and picking a marble from a bag of containing 5 blue, 1 green, and 2 yellow
marbles. Are these events dependent or independent?
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4. Find the following probabilities based on rolling a die and picking a marble from a bag of containing 5
blue, 1 green, and 2 yellow marbles.
a. P(2 and Green) =
b. P(Even and Yellow) =
c. P(# > 2 and Blue) =
d. P(3 and 4) =
5. Consider picking two students from a class where 5 students have red hair, 10 have brown hair, and 8
have blonde hair. Are these events dependent or independent?
6. Find the following probabilities based on the previous class.
a. P(red hair and blonde hair) =
b. P(blonde hair and brown hair) =
c. P(red hair and red hair) =
d. P(not blonde and blonde hair) =
7. Given the data set: 4, 5, 8, 10, 11, 11, 13, 15, 18, 85
a. Find the mean.
b. Find the median.
c. Find the range.
d. Find the IQR.
e. Would you use the mean or median to summarize the data set? Why?
f. Draw a stem and leaf plot.
g. Draw a box and whisker plot.
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Unit 9 Review
Review Question
What is the difference between dependent and independent events?
Independent events – one event doesn’t affect the outcome of the other
Dependent events – one event does affect the outcome of the other
SWBAT review for the Unit 9 test
Discussion
1. How do you study for a test? The students either flip through their notebooks at home or do not
study at all. So today we are going to study in class.
2. How should you study for a test? The students should start by listing the topics.
3. What topics are on the test? List them on the board
- Central Tendencies
- Stem and Leaf Plots
- Box and Whisker Plots
- Graphs: Bar, Line, Circle
- Probability
4. How could you study these topics? Do practice problems
Practice Problems
Have the students do the following problems. They can do them on the dry erase boards or as an
assignment. Have students place dry erase boards on the chalk trough. Have one of the groups explain
their solution.
1. Given the following data set do the following: 2, 4, 6, 6, 7, 8, 9, 10, 10, 10, 11, 11, 12, 12, 69
a. Find the mean, median, mode, and range.
12.5, 10, 10, 67
b. Draw a stem and leaf plot.
c. Draw a box and whisker plot (5 critical values). 2, 6, 10, 11, 69
d. Should you use the mean or median to summarize the data? Why? Median, outlier
2. The following is a summary of the amount of each lunch that was ordered:
pizza: 65, cheeseburger: 8, chicken sandwich: 21, and meatvall hoagie: 34.
a. Draw a bar graph.
b. Calculate what percent each lunch represents.
pizza: 50.7%, cheeseburger: 6.25%, chicken sandwich: 16.4%, meatvall hoagie: 26.5%
c. Draw a circle graph.
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3. The table below shows how much money a policeman made during his first 6 years of working. Draw
a line graph based on the data.
Year
1
2
3
4
5
6
Salary
$40,000
$41,500
$43,000
$43,500
$44,000
$46,500
4. A spinner has the numbers 1 through 20 on it. Numbers 1-3 are green. Numbers 4-9 are yellow.
Numbers 10-18 are blue. Numbers 19-20 are pink. Find the probability of each event. Express each
probability as a fraction then a decimal then a percent.
a. P(15) =
1/20, 0.05, 5%
b. P(yellow) =
6/20, 0.3, 30%
c. P(greater than five) =
15/20, 0.75, 75%
d. P(3 or 4) =
2/20, 0.1, 10%
e. P(green or pink) =
5/20, 0.25, 25%
f. P(even) =
10/20, 0.5, 50%
19
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1
2
3
4
17
16
5
15
6
14
7
13
12
What did we learn today?
20
18
11 10
9
8
Unit 9 Cumulative Review
SWBAT do a cumulative review
Discussion
What does cumulative mean?
All of the material up to this point.
Does anyone remember what the first eight chapters were about? Let’s figure it out together.
1. Pre-Algebra
2. Solving Linear Equations
3. Functions
4. Linear Equations
5. Inequalities
6. Systems
7. Polynomials
8. Factoring
9. Data Analysis
Things to Remember:
1. Reinforce test taking strategies: guess/check, eliminate possibilities, work backwards, and estimating.
2. Reinforce the importance of retaining information from previous units.
3. Reinforce connections being made among units.
In-Class Assignment
1. What set of numbers does -5.4 belong?
a. counting
b. whole
c. integers
d. rationals
2. 3(6 + 2) = 18 + 6 is an example of what property?
a. Commutative
b. Associative
c. Distributive
d. Identity
3. -9.2 + 3.6 =
a. -5.6
b. -12.8
c. -5.4
d. -9.8
b. 10/12
c. 7/24
d. 2/3
b. 2.3
c. 1.8
d. 13.8
b. -11/4
c. -15/4
d. 8/9
1
6
4. 1 
2

4
a. 20/12
5. 12.42 ÷ 5.4 =
a. 4.2
6.  2
1 1
 
2 3
a. -2/12
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7. Which of the following is equal to 83?
a. 8
b. 512
c. 64
d. 128
b. 100
c. 10 2
d. 50
9. 3(1 + 3)2 + 12
a. 60
b. 45
c. 47
d. 28
10. -5x + 15 = 45
a. 6
b. -6
c. 7
d. -7
11. 2x – 3 + 5x = 17 – 3x
a. 2
b. 5
c. Empty Set
d. Reals
8. Which of the following is equal to 200 ?
a. 2 10
12. Which of the following is a solution to y = x + 4 given a domain of {-3, 0, 6}
a. (0, 4)
b. (6, 2)
c. (-3, -10)
d. (-3, 7)
13. Which equation is not a linear equation?
a. y  4 x  2
b.
x
y
4
c.
x2
d.
y  x3  3
c.
x 1
d.
y
14. Which equation is not a function?
a.
y  3x  7
15. If f(x) = 7x + 3, find f(1).
a. 4
b.
y2
b. 7
c. 10
16. Write an equation of a line that passes through the points (0, 6) and (4, 10).
a. y = x
b. y = -x
c. y = x + 6
1
x2
2
d. 19
d. y = x – 6
17. Write an equation of a line that is parallel to y – 3x = 5 and passes thru (5, -2).
a. y = 3x – 17
b. y = 3x
c. y = 3x + 13
d. y = -3x
18. Which of the following is a graph of: y = -2x – 4 .
a.
b.
c.
d.
19. Which of the following is a graph of: y = -3
a.
b.
c.
d.
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20.
x
 3  12
2
a. x < -18
b. x > -18
c. x < 30
d. x < -10
21. |3x – 12| < 12
a. 0 < x< 8
b. x < 0 and x > 8
c. x < 0
d. x< 8
22. |3x – 12| > -8
a. x > -3/4
b. x < 1/2
c. Empty Set
d. Reals
c. (2, 8)
d. (0, 4)
c. (1, 2)
d. (-3, 7)
b. Infinite
c. (1, 1)
d. (-3, 5)
b. 4 x12 y 9
c. 8x12 y18
d. x12 y 9
27. Simplify: (5x – 6) + (3x + 4)
a. 2x – 2
b. 8x – 2
c. 8x – 10
d. 6x2 + 7x + 20
28. Simplify: (4x – 2)(2x + 1)
a. 12x2 + 7x + 8
b. 8x2 – 7x – 8
c. 8x2 + 23x – 2
d. 8x2 – 2
29. (4 x  3)(4 x  3)
a. 16x2 + 24x + 16y2
b. 16x2 – 8x – 16y2
c. 16x2 + 9
d. 16x2 – 9
30. (2 y 2  3) 2
a. 4y4 + 12y2 + 9
b. 4y4 + 9
c. 8x2y4 + 9
d. 6x2 – 7x – 20
23. Solve the following system of equations.
y = 2x + 4
2x + 3y = 28
a. (0, 4)
b. (4/5, 14/5)
24. Solve the following system of equations.
2x – y = 0
5x – 2y = 1
a. (0, 0)
b. (6, 2)
25. Solve the following system of equations.
x – 6y = 5
2x – 12y = 10
a. Empty Set
26. Simplify: (2 y 3 ) 2 ( x 4 y)
a. 4x 4 y 7
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31. 6x(x2 – 4y3)
a. 6x3 + 10xy3
b. 5x3 - 24xy3
c. 6x3 + 8xy3
d. 6x2 – 7x – 20
32. Factor: x2 – 4x – 12
a. (x – 6)(x + 2)
b. (x + 6)(x – 2)
c. (x + 6)(x + 2)
d. (x – 2)(x – 6)
33. Factor: 4x2 – 22x – 36
a. 2(2x2 – 11x – 18)
b. 2(x + 9x – 4)
c. 2x(x + 11x + 18)
d. (2x – 4)(2x – 9)
34. Solve: 4x2 – 36 = 0
a. x = 9
b. x = -3, 3
c. x = -3
d. x = -4, 4
Use the following data set to answer questions 35-37.
2, 2, 4, 6, 8, 10, 10, 10, 20
35. What is the mean?
a. 8
b. 9
c. 20
d. 25
36. What is the median?
a. 2
b. 6
c. 8
d. 10
c. 4
d. 3
37. What is the lower quartile?
a. 12
b. 2
38. There are 4 red marbles, 6 blue marbles, 8 green marbles, and 1 yellow marble in a bag. What is the
probability of picking a blue marble?
a. 4/19
b. 4/20
c. 6/19
d. 14/20
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Standardized Test Review
1. What is the range of the data set?
a. 8
b. 28
c. 29
1
2
3
d. 35
1 1 4 5
0 5 6
1 8 8 9
Key 2 0 = 20
2. The box and whisker plot shown below represents students’ scores on the last algebra test. What is
the best estimate for the percent of students that scored greater than 50 on the test?
40
a. 25%
50
60 70 80 90 100
b. 50%
c. 75%
d. 100%
3. 180 students were surveyed about their favorite sport. The results are shown in the pie chart below.
How many chose hockey?
a. 18
b. 27
c. 32
d. 2700
Favorite Sports
Hockey
15%
Golf
8%
Football
31%
Baseball
19%
Basketball
27%
4. A spinner is divided into 4 equal sized sections. Two are blue, one is red, and one is white. What is
the probability of landing on blue?
a. 25%
b. 50%
c. 33.3%
d. 0%
5. The probability that Tara will make a free throw is 1/2. What is the probability that Tara will make her
next two free throws?
a. 1
b. 1/2
c. 1/4
d. 1/8
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6. The following problems require a detailed explanation of the solution. This should include all
calculations and explanations.
The stem-and-leaf plot below shows a math class’ test scores.
Stems
Leaves
6
0 2 2 4
7
1 3 3 6
8
0 2 3 4 9 9 9
Key: 7|1 = 71
a. Find the mean, median, mode, and range of the data.
b. Find the LE, LQ, UQ, IQR, and UE of the data.
c. Should you use the mean or median to summarize the data.
Jacob Louis Trombetta © 2013
All Rights Reserved
365