Download Math: Algebra 1A Name: Unit 2: Statistics Date: Day 1 – Frequency

Math: Algebra 1A
Name: ______________________________
Unit 2: Statistics
Date: _______________________________
Day 1 – Frequency and Cumulative Frequency Tables
WARM-UP
1) Given the chart below, answer the following questions that will help you understand
frequency tables:
a) How many trees are between 26 feet and 50 feet? ___
b) Can you determine the exact number of trees that are
between 53 feet and 75 feet? If so, what is it? If not,
explain.
Frequency Tables
There are many ways to organize and visually display data. Sometimes it is helpful to organize numerical
data into intervals.
*Frequency means how often something occurs.
The frequency of an interval is the number of data values that are in that interval.
A frequency table groups a set of data values into intervals and shows the frequency for each interval.
Intervals in frequency tables do not overlap, do not have any gaps and are usually of equal size!
Cumulative Frequency Tables
Cumulative frequency tables show, in each interval, the accumulation of the number of data
values for each preceding interval. It is a running total of the frequencies.
NOTE: The intervals in a Cumulative Frequency Table will always start with the same number!!!
If frequency tables are supplied, we must create a column for the new cumulative intervals.
To find the frequency for each interval in the frequency table, subtract each cumulative
frequency from the cumulative frequency that comes before it.
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Example #1: The Malden High School Varsity Boy’s basketball team had an excellent season,
compiling a record of 15 – 5 (15 wins and 5 losses). The total points scored by the team for
each of the 20 games are listed below in the order in which the games were played:
76, 55, 76, 64, 46, 91, 65, 46, 45, 53, 56, 53, 57, 67, 62, 64, 67, 52, 58, 62
Complete the frequency table below.
Example #2: The data below represents the numbers of hours per week a group of students
spent watching television.
a) Determine four appropriate intervals (the first is given) and fill in the frequency table using
the given data.
7, 10, 1, 5, 14, 22, 6, 8, 0, 11, 13, 3, 4, 14, 5
Interval of
Tally
Frequency
Hours
a) Which interval contains the lowest number of hours per week? __________________
b) What percent of students watch 12-17 hours of television? ____________________
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Example #3: The number of text messages sent on one day by different students are shown
below. Create a frequency table using intervals of 10. Plan ahead to create appropriate
intervals.
17, 3, 1, 30, 11, 7, 1, 5, 2, 39, 22, 13, 2, 0, 21, 1,
49, 41, 27, 2, 0
Cumulative
Cumulative
Intervals
Frequency
To the right of the frequency table, create a cumulative frequency table for the number of
text messages sent on one day by different students, then answer the questions below.
a) Which interval represents the greatest number of texts sent by students? __________
b) What percent of students are texting under 30 times in one day? Round to the nearest
hundredth of a percent. ___________
Example #4: Using the cumulative frequency table for the scores received on an Algebra quiz,
answer the questions below. (STOP! What do you notice about the intervals?)
a) How many students took the quiz? ______
b) Students receive an A if they earned a 90% or better
on the quiz. How many students received an A?
c) What percentage of students received an A?
Round to the nearest thousandth percent.
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Example #5: Shaker High School gave a final exam to all students taking Forensics. The total
number of students taking this examination was 180. The test grades for these students were
grouped into the table on the left below.
a) Fill in the Cumulative Frequency Table.
b) What must the last entry of the cumulative frequency table always be equal to? Explain.
*Example #6: A statistics class surveyed some students during one lunch period to obtain
opinions about television programming preferences. The results of the survey are summarized
in the table below.
a) How many male students were surveyed? _______
b) How many of the male students surveyed prefer comedy? _______
c) Based on the sample, predict how many of the school's 351 males would prefer comedy.
Justify your answer.
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*Example #7: The school newspaper surveyed the student body for an article about club
membership. The table below shows the number of students in each grade level who belong to
one or more clubs.
If there are 180 students in ninth grade, what percentage of the ninth grade students belong
to more than one club?
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Day 1 HW - Frequency and Cumulative Frequency Tables
1. Mrs. Hopkins recorded her students’ final exam scores in the frequency table below. She
used a tally column to count the number of scores in each interval, then she counted the
tally marks to make the entries in the frequency column. Using the table below, determine
how many students took Mrs. Hopkins’ final exam. _________
2. The following set of data represents the scores on a mathematics quiz:
58, 79, 81, 99, 68, 92, 76, 84, 53, 57, 81, 91, 77, 50, 65, 57, 51, 72, 84, 89
Complete the frequency table below using the given data.
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3. The Fahrenheit temperature readings on 30 April mornings in Stormville, New York, are
shown below:
41°, 58°, 61°, 54°, 49°, 46°, 52°, 58°, 67°, 43°, 47°, 60°, 52°, 58°, 48°, 44°, 59°, 66°, 62°,
55°, 44°, 49°, 62°, 61°, 59°, 54°, 57°, 58°, 63°, 60°
Using the data, complete the frequency table below.
4. The test scores for 18 students in Ms. Mosher’s class are listed below:
86, 81, 79, 71, 58, 87, 52, 71, 87, 87, 93, 64, 94, 81, 76, 98, 94, 68
Using the data complete the frequency table below.
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5. College students spent the following amounts of money on textbooks for one semester:
$101, $107, $121, $90, $89, $101, $98, $110, $115, $85, $95, $109, $109, $110, $109
Complete the Frequency and Cumulative Frequency tables for the given data.
Cost
Interval
6.
Tally
Frequency
Cost
Cumulative
Interval
Frequency
80-89
80-89
90-99
80-99
100-109
80-109
110-119
80-119
120-129
80-129
The following data consists of the weights, in pounds, of 24 high school students:
195, 206, 100, 98, 150, 210, 195, 106, 195, 108, 180, 212, 104, 195, 100, 216, 99, 206, 116,
142, 100, 135, 98, 160
Complete the Frequency and Cumulative Frequency tables for the given data. In the
Cumulative Frequency chart, you must first come up with (4) appropriate Weight Intervals.
Weight
Interval
Tally
Frequency
51-100
101-150
151-200
201-250
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Weight
Cumulative
Interval
Frequency
7. The table below lists the heights of students, in inches, in Mrs. McCarthy’s 2nd period class.
Fill in the Cumulative Frequency Table with the correct Intervals and Cumulative Frequency.
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Day 2 – Two Way Frequency Tables
WARM-UP
The table below shows a cumulative frequency distribution of runners' ages.
1) According to the table, how many runners are in their forties?
(A) 25
(B) 10
(C) 7
(D) 6
2) How many total runners are there? _____________
3) What percent of runners are between the ages of 20-49? ____
Two-Way Frequency Table (displays “counts”)
Two-way frequency tables are a visual representation of the possible relationships between
two sets of categorical data. The categories are labeled at the top and the left side of the
table, with the frequency (count) information appearing in the interior cells of the table. The
"totals" of each row appear at the right, and the "totals" of each column appear at the bottom.
A survey asked, "If you could have a new vehicle, would you want a sport utility vehicle or a
sports car?
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Example #1: Felipe surveyed students at his school. He found that 78 students own a cell
phone and 57 of those students own an MP3 player. There are 13 students that do not own a
cell phone, but own an MP3 player. Nine students do not own either device. Construct a two-way
table summarizing the data.
Step 1: Use the values given to fill in the table.
Step 2: Use reasoning to complete the table. Remember, the totals are for each row and
column. The column labeled “Total” should have the same sum as the row labeled “Total.”
Example #2: There are 150 children at summer camp and 71 signed up for swimming. There
were a total of 62 children that signed up for canoeing and 28 of them also signed up for
swimming. Construct a two-way table summarizing the data.
Canoeing
No Canoeing
Swimming
No Swimming
Total
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Total
Example #3: Below is a two-way frequency table that shows the eye color of boys and girls in
Mrs. G’s Algebra Class. Fill out the chart and answer the following questions.
Brown
Boys
Blue
4
Girls
Total
4
Green
Total
2
13
5
7
1) How many students are in the class? ____
3) How many boys have blue or green eyes?____
2) How many students have green eyes? ___
4) How many students don’t have blue eyes?___
More Practice: Use the information to construct a two-way frequency table.
1) There were 100 customers in a restaurant that were asked whether they liked chicken or
beef and whether they liked rice or pasta. Out of 30 customers that liked rice, 20 liked
chicken. There were 60 customers that liked chicken.
Rice
Pasta
Total
Chicken
Beef
Total
2) As each person entered the theater, Aaron counted how many of the 105 people had
popcorn and how many had a drink. He found that out of 84 people that had popcorn, only 10
did not have a drink. Six people walked in without popcorn or a drink.
Drink
No Drink
Popcorn
No Popcorn
Total
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Total
Important Definitions Regarding Two-Way Frequency Tables
Joint Frequencies: Entries (frequency count) in the body of the table.
Marginal Frequencies: Entries (frequency count) in the “Total” row and “Total” column. (Hint:
Think “margins” when finding the marginal frequencies!)
A survey asked the questions “What superpower would you want to have?” The results are given
in the table below.
To Fly
To Freeze
Invisibility
Things
Super
Telepathy
Total
Strength
Females
12
15
A
5
B
55
Males
12
16
10
C
3
45
Total
24
31
25
9
D
100
1) In the chart above, cells A, B, C and D need filled in with numbers. Using the given
table, find the numerical value for: A: _____ B: _____ C: _____ D: _____
2) Of the cells A, B, C and D, which cells represent Joint Frequencies? _____________
3) Of the cells A, B, C and D, which cells represent Marginal Frequencies?____________
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Day 2 HW -Two Way Frequency Tables
1) Eighth grade students were asked whether they participate in an after-school activity.
Complete the two-way frequency table below.
2) The table shows the results of a survey about what the engineers said their favorite
subject was in middle school.
a) How many chemical engineers chose science? ________________
b) How many engineers chose math? _______________
c) Overall, what was the favorite subject of all engineers? _________________
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3) Below you will find an incomplete two-way frequency table that shows the number of girls
and boys that were passing Economics and Science. There are a total of 72 boys and 72 girls
taking Economics. There are 78 boys and 60 girls taking Science.
a) Complete the table.
b) How many boys passed Economics and Science? __________
c) How many girls did not pass Science or Economics? _________
d) How many students passed Science? ___________
e) How many of the students are boys? ___________
f) How many total students are there? ____________
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Day 3 - Two-Way Relative Frequency
Two-Way Relative Frequency Table (“percentages”)
When a two-way table displays percentages or ratios (called relative frequencies), instead of
just frequency counts, the table is referred to as a two-way relative frequency table. These
two-way tables can show relative frequencies for the whole table, for rows, or for columns.
Typically when using the table the relative frequencies may be displayed as a ratio, a decimal
(to nearest hundredth), or percent (to nearest percent).
If the two-way relative frequency is for the whole table, each entry in the table is divided by
the total count (found in the lower right corner). The ratio of "1", or 100%, occurs only in the
cell in the lower right corner.
Two-Way Conditional Relative Frequency (“percentages” by row or column)
When a relative frequency is determined based upon a row or column, it is called a "conditional"
relative frequency. To obtain a conditional relative frequency, divide a joint frequency (count
inside the table) by a marginal frequency total (outer edge) that represents the condition
being investigated. You may also see this term stated as row conditional relative frequency or
column conditional relative frequency.
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How many people responded to the survey? _______
How many males responded to the survey? _______
How many people chose an SUV? ______
How many females chose a sports car? _______
How many males chose an SUV? ________
What percentage of the survey takers were female? ________
What is the relative frequency of males choosing a sports car? __________
Was there a higher percentage of males or females choosing an SUV? _____________
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1) Convert the two-way frequency table below into a two-way relative frequency table.
2)
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3) The citizens of Parkdale are preparing to vote on a bond issue to fund an expansion of the
public library. The table below records data about support for the bond issue.
For all the following, calculate the conditional relative frequency for all people in the given age
group. Write answers as a ratio and then a percent.
a) The people between 18 and 25 who support the bond issue.
b) The people between 26 and 64 who support the bond issue.
c) The people 65 or older who oppose the bond issue.
d) The people between 26 and 64 who oppose the bond issue.
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4) A public opinion survey explored the relationship between age and support for increasing
the minimum wage. The results are found in the following two-way frequency table.
Fill in the missing data in the table. Then calculate the relative frequencies below (round all
answers to the nearest percent).
1. Out of the people that have no opinion, what percentage is over 60 years old?
2. What percentage of the people surveyed is for increasing minimum wage?
3. How many people over 60 are against increasing the minimum wage?
4. For ages 21-60 how many were not against increasing the minimum wage?
5. What percent of people over 60 are against or have no opinion?
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Day 3 HW -Two Way Relative Frequency
1) The two-way table shows the number of students that do or do not do chores at home and
whether they receive an allowance or not.
a. How many total students do chores? _________
b. What is the relative frequency of students that do chores and get an allowance to the
number of students that do chores? Round to the nearest hundredth if necessary. ______
c. What is the relative frequency of students that do not do chores nor get an allowance to
the total number of students? Round to the nearest hundredth if necessary. ___________
2) The two-way table shows the number of Sasha’s soccer teammates that are in her Math
class and English class.
a. How many teammates does Sasha have? ___________
b. What is the relative frequency of teammates that are in both of Sasha’s classes to all of
her teammates? ______________
c. Of the teammates in her math class, which percentage is higher: the percentage of
teammates that are in her English class or the percentage of teammates that are not in her
English class? _______________
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3) A survey was conducted of people leaving a local restaurant to see who ordered the most
desserts. Here are the findings:
Dessert
No Dessert
Women
185
115
Men
204
190
Totals
Totals
a.) Complete the chart above.
b.) What percent (rounded to the nearest tenth) of the people are female and order
dessert? ____________
c.) What percent (rounded to the nearest hundredth) of males do not order dessert? ____
4) Suppose you are randomly assigned a hotel room at the Zippy Hotel in Florida for Spring
Break. Use the chart to answer the following questions.
a) Complete the chart above by filling in the blanks of the missing cells.
b) What percent (rounded to the nearest tenth) of rooms are 3 room luxury suites with
an ocean view? __________
c) What percent (rounded to the nearest hundredth) of ocean view rooms are 2
bedrooms? __________
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Day 4 – Measures of Central Tendency and Dispersion
WARM-UP
Below is the data for eye color of girls and boys in Mr. A’s class. Fill in the missing blank cells
then answer the questions.
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Measures of Central Tendency
You can use different measures to interpret and compare sets of data.
One way to summarize the data is to use a measure of central tendency. Mean, median and
mode are all measures of central tendency.
* The measure of central tendency that best describes a data set may depend on whether the
data set has an outlier. An outlier is a data value that is much greater or less than the other
values in the set. The mean is HIGHLY affected by outliers. In the case of outliers, always
use the median to best describe the data.
Measures of Dispersion
A measure of dispersion describes how dispersed, or spread out, the values in a data set are.
One measure of dispersion is range.
The range of a set of data is the difference between the greatest and least data values.
Example #1: Alex earned scores of 60, 74, 82, 87, 87, and 94 on his first six algebra tests.
What is the relationship between the measures of central tendency of these scores?
(1) median < mode < mean
(3) mode < median < mean
(2) mean < mode < median
(4) mean < median < mode
Example #2: The closing prices, in dollars, of two stocks for the first five days in February are
shown below, with the mean of each set given.
Stock A: 25,30,30,47,28
Stock B: 34,28,31,36,31
a) Find the range of each stock.
b) Use the results of the range to compare the data sets.
c) What do you notice about the averages of each stock? Could you use this information to
compare the data sets? Explain.
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Example #3: Students in Mr. Mason’s statistics class were trying to determine if people speed
along a certain section of roadway. They collected speeds of 20 vehicles, as displayed in the
table below.
a) Find the mean, median, and mode for this data set.
b) The speed limit along this part of the highway is 35 mph. Based on your results from
part a, is it fair to make the conclusion that the average driver does speed on this
roadway?
Using Your Graphing Calculator To Find The Mean, Median and Mode
Given the data set {13, 3, 10, 9, 7, 10, 12, 8, 6, 3, 9, 6, 11, 5, 9, 13, 8, 7, 7} find the mean and median.
1-
Enter the data into a list.
Press STAT. Choose option #1: Edit.
Enter your data values under L1.
2 - Press STAT. Arrow to the right to CALC. Now choose option #1: 1-Var Stats. When
1-Var Stats appears on the home screen, tell the calculator the name of the list you are using (such
as: 1-Var Stats L1). Press ENTER. Arrow up and down the screen to see the statistical information.
**Although the mode will not appear in this information, you can sort the data into ascending order
to help find the mode. STAT, #2 SortA (, and specify L1, or the list you are using.
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Example #4: Use the picture below and your graphing calculator to answer the following
questions.
a) What are the mean, median, and mode of the bowling scores below? Which measure of
central tendency best describes the scores?
b) Consider the scores from above that do not include the outlier of 189. What are the mean,
median, and mode of the scores? Which measure of central tendency best describes the data?
Example #5: Find the value of x, of 2x, x, x + 3, and 4x + 7, if the mean is 50.
Example #6:
a) Your grades on three exams are 80, 93, and 91. What grade do you need on the next exam
to have an average of 90 on the four exams?
b) If 100 is the highest possible score on the fourth exam, is it possible to raise your average
to 92? Explain.
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*Example #7: Isaiah collects data from two different companies, each with four employees.
The results of the study, based on each worker’s age and salary, are listed in the tables below.
Which statement is true about these data?
1 The median salaries in both companies are greater than $37,000.
2 The mean salary in company 1 is greater than the mean salary in company 2.
3 The salary range in company 2 is greater than the salary range in company 1.
4 The mean age of workers at company 1 is greater than the mean age of workers at
company 2.
*Example #8: The table below shows the annual salaries for the 24 members of a professional
sports team in terms of millions of dollars.
The team signs an additional player to a contract worth 10 million dollars per year. Which
statement about the median and mean is true?
1 Both will increase.
2 Only the median will increase.
3 Only the mean will increase.
4 Neither will change.
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Example #9: What will happen to the measures of central tendency if we add the same amount
to all data values, or multiply each data value by the same amount?
Data
Original Data
Set:
Mean
Mode
Median
6, 7, 8, 10, 12, 14, 14, 15, 16, 20
Add 3 to
each data
value
Multiply 2
times each
data value
When added: Since all values are shifted the same amount, the measures of central tendency
all shifted by the same amount. If you add 3 to each data value, you will __________ to the
mean, mode and median.
When multiplied: Since all values are affected by the same multiplicative values, the measures
of central tendency will feel the same affect. If you multiply each data value by 2, you will
_____________ the mean, mode and median by ________.
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Day 4 HW - Measures of Central Tendency and Dispersion
1) Find the mean, median, and mode of each data set. Tell which measure of central tendency
best describes the data. Weights of books (oz): 12, 10, 9, 15, 16, 10
2) Find the value of x such that the data set has a mean of 91.
99, 86, 76, 95, x
3) Set A: 0, 12, 7, 19, 21
Set B: 13, 16, 15, 17, 12
a) Find the range of each data set.
b) Find the mean of each data set.
c) If the means for the two sets are similar, is this a good measurement to use to compare the
two sets? Why or why not?
4) Which of the following data sets has no mode?
(1) {4, 7, 8, 9, 10}
(3) {1, 1, 2, 3, 4, 4}
(2) {2, 2, 3, 3, 4, 4}
(4) {2, 2, 4, 5, 7, 8}
5) Which statement is true about the data set 3, 4, 5, 6, 7, 7, 10?
(1) mean = mode
(3) mean = median
(2) mean > mode
(4) mean < median
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6) The mean of a set of four numbers is 78. If three of the numbers in the set are 71, 74, and
83, what is the fourth number?
7) In Mr. Klein’s Calculus Course, eight students recently took a test. Their grades were as
follows: 45, 78, 82, 85, 87, 89, 93, 95
a) Calculate the mean and median of this data set.
b) What score is an outlier in this data set?
c) Which value, the mean or the median, is a better measure of how well the average student
did on Mr. Klein’s quiz? Explain.
d) If Mr. Klein awarded everyone 2 bonus points, how would that affect the mean, median and
mode?
e) If Mr. Klein doubled everyone’s score, how would that affect the mean, median and mode?
8) The prices of seven racecars sold last week are listed in the table below.
a) What is the mean value of these racecars, in dollars?
b) What is the median value of these racecars, in dollars?
c) What is the mode of these racecars, in dollars?
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Day 5 – Dot Plots (Line Plots) with Measures of Central Tendency and Dispersion
Dot Plots
Dot Plots (aka Line Plots) are defined as statistical charts consisting of data points plotted on
a simple scale, depicting distributions. Typically dot plots use filled in circles or x’s.
Dot Plots are one of the simplest statistical plots and are suitable for small sized data sets. If
dealing with larger data sets, we refer to a histogram or a box-and-whisker plot.
Example #1: Each person in a random sample of ten 9th graders was asked the question, “How
many hours did you spend watching TV last night?” The data is given below.
Construct a dot plot of the data on hours of TV.
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Example #2: The results of a survey on the number of televisions in students’ households are
shown in the dot plot.
a) Calculate the mean, median, and range of the data.
b) How can you tell from the graph that the mean and the median are equal?
c) How can you tell from the graph that the median and the mode are equal?
Example #3: The dot plot below shows the number of people in a small town who own a certain
number of footballs. So, for example, there are 5 people who own 1 football and 7 people who
own 2 footballs. Find the mean, median, and mode.
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*Example #4: Robin collected data on the number of hours she watched television on Sunday
through Thursday nights for a period of 3 weeks. The data are shown in the table below.
Using an appropriate scale on the number line below, construct a box plot for the 15 values.
Move to end of packet (Day 7 Box Plots)
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Day 5 HW - Dot Plots with Measures of Central Tendency and Dispersion
1) Match the solutions to the problems below. Write the letters of your answer in the blank
spaces at the bottom of the page. Your answers will spell out the names of the two
mathematicians who are credited with the founding of probability theory!
Use the following data sets.
Data Set 1: 7, 11, 5, 9, 7, 19, 8, 13, 2
Data Set 2: 84, 78, 66, 93, 68, 72, 96, 88, 96, 89
1. The mean of Data Set 1
A. 7
2. The median of Data Set 1
C. 86
3. The mode of Data Set 1
E. 96
4. The maximum of Data Set 1
F. 30
5. The range of Data Set 1
L. 8
6. The mean of Data Set 2
M. 83
7. The median of Data Set 2
P . 19
8. The mode of Data Set 2
R. 9
9. The minimum of Data Set 2
S. 17
10. The range of Data Set 2
T. 66
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Place all Work Below:
(2) The dot plot shows the number of students in each homeroom at Jefferson High
School.
a) Find the mean, median and range of the data.
b) How can you use the dot plot to determine whether the mean and median
are equal?
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Day 6 – Dot Plots and Standard Deviation
WARM-UP
1) Thirty female users were selected at random from a database of people who play a
leadership skill game regularly. The table of the recorded scores are below.
Using the scale below, make a dot plot representing the data scores above. Notice that you
have some data values between the scales provided!
Standard Deviation
So far, you have learned about one measure of dispersion, range. Another measure of dispersion is
standard deviation. Standard deviation is a measure of how the values in a data set vary, or deviate,
from the mean.
***The SMALLER the standard deviation, the more CLUSTERED it is around the mean.
***The LARGER the standard deviation, the more SPREAD OUT the data values are from the mean.
The special symbol used for standard deviation is  . This is a Greek letter known as sigma.
Standard deviation is found in the graphing calculator. We will find the mean X in the graphing
calculator as well!
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Steps for finding the Mean and the Standard Deviation in the Calculator.
1) From the home screen, press STAT, ENTER to access the stat editor.
2) If there are already numbers in L1, clear the data from L1 by moving the cursor to “L1”
and pressing CLEAR, ENTER.
3) Move the cursor to the first element of L1, type the first data value, and press enter.
Continue entering the remaining data values into L1 in the same way.
4) Press 2ND, QUIT to return to the home screen.
5) Press STAT, select CALC, select 1-Var Stats, press ENTER.
6) The screen should now show summary statistics for your data set. The mean is the X
value and the standard deviation is the  X value.
Example #2: Using a graphing calculator, find the mean and standard deviation of each data
set. Round to the nearest hundredth.
a) Data Set 1: 4,8,5,12,3,9,5,2
Data Set 2: 5,9,11,4,6,11,2,7
Mean: Data Set 1: ______
Standard Deviation: Data Set 1: ______
Data Set 2: ______
Data Set 2: ______
Which data set has a greater standard deviation? Explain what that means.
b) Data Set 1: 8.2, 11.6, 8.7, 10.6, 9.4, 10.1, 9.3 Data Set 2: 9.3, 10.2, 8.1, 12.3, 8.7, 9.9, 10.1
Mean: Data Set 1: ______
Standard Deviation: Data Set 1: ______
Data Set 2: ______
Data Set 2: ______
Which data set has a greater standard deviation? Explain what that means.
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Example #3: Three data sets are shown in the dot plots below.
a) Which data set has the smallest standard deviation of the three? Explain.
b) Which data set has the largest standard deviation of the three? Explain.
c) Using the calculator, find the standard deviation of Data Set 1: ________________
d) Using the calculator, find the standard deviation of Data Set 2: ________________
e) Do your answers from parts c and d, prove parts a and b to be true? ____________
Example #4: a) Comparing the histograms below, which city would have the larger standard
deviation? Why?
*Example #5: The two sets of data below represent the number of runs scored by two
different youth baseball teams over the course of a season.
Team A: 4, 8, 5, 12, 3, 9, 5, 2
Team B: 5, 9, 11, 4, 6, 11, 2, 7
Which set of statements about the mean and standard deviation is true?
1 mean A < mean B standard deviation A > standard deviation B
2 mean A > mean B standard deviation A < standard deviation B
3 mean A < mean B standard deviation A < standard deviation B
4 mean A > mean B standard deviation A > standard deviation B
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Day 6 HW - Dot Plots and Standard Deviation
For 1-2, using a graphing calculator find the mean and standard deviation of each data set.
Round to the nearest hundredth.
1) Data set 1: 102, 98, 103, 86, 101, 110
Mean: Data Set 1:
Data set 2: 90, 89, 100, 97, 102, 97
______
Standard Deviation: Data Set 1: ______
Data Set 2: ______
Data Set 2: ______
2) Data set 1: 32, 40, 35, 28, 42, 32, 44
Mean: Data Set 1:
Data set 2: 40, 38, 51, 39, 46, 40, 52
______
Standard Deviation: Data Set 1: ______
Data Set 2: ______
Data Set 2: ______
3) Determine which data set has a greater mean and greater median. Explain.
4) Ten people attended a talk at a conference. At the end of the talk, the attendees were
given a questionnaire that consisted of four questions. The questions were optional, so it
was possible that some attendees might answer none of the questions while others might
answer 1,2,3 or all 4 of the questions. The possible numbers of questions answers are 0,1,2,3
and 4. Suppose that the numbers of questions answered by each of the ten people were as
shown in the dot plot below.
Use the calculator to find the mean and the standard deviation of the data set.
Mean: _______________
Standard Deviation: ___________________
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5) Two students were comparing their grades on their report cards.
Clara: 83, 92, 79, 66, 82, 85
Julia: 83, 75, 78, 86, 77, 87
a.) Which student, if either, has the higher mean average? Round to the nearest tenth.
b.) For Clara’s grades, calculate the standard deviation to the nearest tenth.
c.) For Julia’s grades, calculate the standard deviation to the nearest tenth.
d.) Which student has the greater dispersion (i.e. grades are more spread out)?
6) The heights of a painter’s ladders are 12 ft, 8 ft, 4 ft, 3 ft, and 6 ft. What are the mean,
median, mode, and range of the ladder heights?
7) Find the value of x such that the data set has the given mean.
a) 11, 12, 5, 3, x ; mean 7.4
b) 55, 60, 35, 90, x ; mean 51
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Day 7 CW/HW – Box Plots
WARM-UP
a) The heights (in inches) of 9 women are shown below.
68.4
70.9
67.4
67.7
67.1
69.2
66.0
70.3
67.6
Using your calculator, find the mean and standard deviation of these heights to the nearest
hundredth.
b) Using the given set of numbers, find the following:
Maximum:
Minimum:
125, 80, 140, 135, 126, 140, 350, 75
Range:
Median:
Today we are going to extend our knowledge of the data set in the warm-up above, by plotting
box plots. After understanding the central tendency of a data set, it is important to
understand how the rest of the data set is distributed.
Quartiles
Quartiles are numbers that separate a set of scores into 4 equal groups; each group contains ¼
or 25% of the original number of scores.
First Quartile (Q1):
Second Quartile (Q2) (Also known as the median):
Third Quartile (Q3):
Interquartile range: difference between the third and first quartile.
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Steps for finding the Minimum, Quartiles, Median and Maximum in the Calculator.
1. From the home screen, press STAT, ENTER to access the stat editor.
2. If there are already numbers in L1, clear the data from L1 by moving the cursor to “L1”
and pressing CLEAR, ENTER.
3. Move the cursor to the first element of L1, type the first data value, and press enter.
Continue entering the remaining data values to L1 in the same way.
4. Press 2ND, QUIT to return to the home screen.
5. Press STAT, select CALC, select 1-Var Stats, press ENTER.
6. The screen should now show summary statistics for your data set. Arrow down to find
the following values: minX (Minimum), Q1 (First Quartile), Med (Median or Second
Quartile/Q2), Q3 (Third Quartile), maxX (Maximum).
Re-visit the warm-up: Find the first quartile, third quartile, and Interquartile range of the
following data. Show a check in the calculator!
Using the given set of numbers, find the following:
Maximum: 350
Minimum: 75
First Quartile (Q1):
Median (Q2): 130.5
Third Quartile (Q3):
Interquartile Range:
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125, 80, 140, 135, 126, 140, 350, 75
Example #1: What are the minimum, first quartile, median, third quartile and maximum of the
data set below?
95, 85, 75, 85, 65, 60, 100, 105, 75, 85, 75
Maximum:
Minimum:
First Quartile (Q1):
Median (Q2):
Third Quartile (Q3):
Box Plots
A box plot (formally called the box-and-whisker plot) is a graph that summarizes a set of data
by displaying it along a number line. It consists of three parts: a box and two whiskers.
Example #2: The following box plot gives the results on a recent SAT math test.
a) What value represents 25% of data?_____
b) What value represents 50% of data?_____
c) What value represents 75% of data?_____
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Example #3: Using the same data set construct a box plot on the given number line.
52, 60, 66, 66, 68, 72, 72, 73, 74, 75, 80, 82, 84, 91, 92, 98
minimum:
lower quartile:
maximum:
upper quartile:
median:
interquartile range:
Example #4: Below are the number of hours a student worked each week at her summer job.
When she applied for the job she was told the typical work week was 29 hours.
29, 23, 21, 20, 17, 16, 15, 33, 33, 32, 15
minimum:
lower quartile:
median:
upper quartile:
maximum:
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*Example #5: Christopher looked at his quiz scores shown below for the first and second
semester of his Algebra class.
Semester 1: 78, 91, 88, 83, 94
Semester 2: 91, 96, 80, 77, 88, 85, 92
Which statement about Christopher's performance is correct?
1 The interquartile range for semester 1 is greater than the interquartile range for
semester 2.
2 The median score for semester 1 is greater than the median score for semester 2.
3 The mean score for semester 2 is greater than the mean score for semester 1.
4 The third quartile for semester 2 is greater than the third quartile for semester 1.
*Example #6: Corinne is planning a beach vacation in July and is analyzing the daily high
temperatures for her potential destination. She would like to choose a destination with a high
median temperature and a small interquartile range. She constructed box plots shown in the
diagram below.
Which destination has a median temperature above 80 degrees and the smallest interquartile
range?
1 Ocean Beach
2 Whispering Palms
3 Serene Shores
4 Pelican Beach
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Example #7: Create a box plot using the data shown in the dot plot below.
minimum:
lower quartile:
median:
upper quartile:
maximum:
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