Download Algebra 1B Assignments Data, Statistics, and Probability

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Algebra 1B Assignments
Data, Statistics, and Probability
Review
Worksheet: Interpreting Graphs
1-6a
Pages 43-45: #1-13, 24, 25, 27, 28, 38, 39
Page 637: #1-4
1-6b
Worksheet: Box Plot and Outlier Rule
1-6c
Worksheet: Dot Plot and Histogram
2-6
Pages 96-98: #1-28, 43, 46-50, 57-60
Quiz
Data and Statistics
2-7
Pages 104-105: #2-20 even, 21-31, 36-41
Review
Worksheet: Data, Statistics, Probability
Test
Data, Statistics, and Probability
Section 1-6a
Warm – Up:
Simplify.
1. 8  3(11  6)
2. 9  16  4(7  5)
3. 4 x  (7 10 x)
4. 5(6x  2)  3(1  4 x)  8x
Objective: To find mean, median, mode, range, standard deviation, and outliers
Measures of Central Tendency:
 Mean: sum of all the data items divided by number of data items
 Median: middle value when data is listed in order from least to greatest
 Mode: data item that occurs the most
Measures of Spread:
 Range: greatest data value - least data value
 Standard Deviation: measure of how the data varies from the mean
STAT
EDIT
enter numbers in L1
STAT
CALC (enter)
1-VAR STAT (enter, enter)
x
 Outlier: data value that is much higher or lower than the other data values
(over 2 standard deviations from the mean)
Example #1:
Data set: 4, 10, 5, 8, 6, 2, 22, 7
a) Calculate the mean, median, mode, range, standard deviation, and outliers.
mean =
median =
mode =
range =
SD =
outliers =
b) Which measure of central tendency best describes the data set? Why?
* Mean is used to describe the middle set of data that does not have an outlier.
* Median is used to describe the middle set of data that does have an outlier.
Example #2:
Data set: 45, 34, 48, 36, 56, 48, 27, 39, 36
a) Calculate the mean, median, mode, range, standard deviation, and outliers.
mean =
median =
mode =
range =
SD =
outliers =
b) Which measure of central tendency best describes the data set? Why?
Example #3:
Suppose your grades on three science exams are 82, 94, and 89. What grade do you need on
your next exam to have an average of 90? Show your work.
Closure Question:
When should the mean be used and when should the median be used to describe data?
Section 1-6b
Warm – Up:
Calculate the mean, median, mode, range, and standard deviation for the following data:
12, 10, 9, 15, 16, 10
mean =
median =
mode =
range =
SD =
Objective: To display data using a box-and-whisker plot
To use the 1.5 IQR rule to determine outliers
box-and-whisker plot: a data display that divides a set of data into four parts
 lower quartile (Q1) - median of lower half
 middle quartile (Q2) – median
 upper quartile (Q3) - median of upper half
* How to calculate outliers: (use the 1.5 IQR rule)
IQR (Interquartile Range) = Q3 - Q1

Q1 - 1.5(Q3 - Q1)
 Q3 + 1.5(Q3 - Q1)
Example #1:
The following is a list of hours college students study in a week:
12, 15, 19, 6, 23, 13, 1, 15, 18, 10, 13, 16, 14
a) Rewrite the list of data in order from least to greatest.
b) Determine the 5-number summary (minimum, lower quartile, median, upper quartile, and maximum).
min =
Q1 =
median =
Q3 =
max =
c) Make a box-and-whisker plot.
d) What numbers are in the bottom 75% of hours?
e) What percentage of hours is between 14 and 23?
f) Use the 1.5 IQR rule to determine if there are outliers.
g) If there are outliers: How would the center (mean, median, mode), spread (range, standard
deviation), and shape (symmetry) change if there were not outliers?
If there are not outliers: How would the center (mean, median, mode), spread (range,
standard deviation), and shape (symmetry) change if there were outliers?
mean =
median =
mode =
range =
SD =
symmetry =
Example #2:
The following is a list of average monthly rainfalls in different cities in millimeters.
122, 143, 70, 98, 84, 126, 114, 98, 85, 104, 71, 77, 111, 108
a) Determine the 5-number summary and make a box-and-whisker plot.
b) What numbers are in the middle 50% of monthly rainfalls?
c) What percentage of monthly rainfalls is between 70 and 84?
d) Use the 1.5 IQR rule to determine if there are outliers.
e) If there are outliers: How would the center (mean, median, mode), spread (range, standard
deviation), and shape (symmetry) change if there were not outliers?
If there are not outliers: How would the center (mean, median, mode), spread (range,
standard deviation), and shape (symmetry) change if there were outliers?
mean =
median =
mode =
range =
SD =
symmetry =
Closure Question:
In a box-and-whisker plot, what percentage of the numbers is between the lower quartile
and the maximum?
Section 1-6c
Warm – Up:
Data set: 8, 14, 5, 17, 11, 25, 13, 2, 7, 15
1) Make a box-and-whisker plot for the data set.
2) What numbers are in the top 75% of data?
3) Use the 1.5 IQR rule to determine if there are outliers.
Objective: To display data using a dot plot and a histogram
dot plot: A data display with dots above a number line corresponding to the location of each
item.
Example #1:
Mrs. Ortiz is planning a garden. She asked her class how many rosebushes they want.
Their answers are listed below.
2, 3, 5, 4, 4, 1, 3, 2, 6, 4, 3, 4, 2, 2, 4
a) Make a dot plot for the data set.
b) Determine the mean, median, mode, range, and standard deviation.
mean =
median =
mode =
range =
SD =
histogram: A bar graph that shows the number of times a data item occurs. Data is
combined into intervals of equal size. The intervals touch, but do not overlap.
Example #2:
The histogram shows the amount of money that 50 customers spent at a grocery store.
a) What is the greatest amount of money that any customer spent?
b) Which interval represents the greatest number of customers?
c) How many customers spent less than $40?
Example #3:
The data shows the number of hours of battery life for different brands of batteries used in
portable CD players. Use the data to make a histogram.
12, 9, 10, 14, 10, 11, 10, 18, 21, 10, 14, 22
 Step 1: Decide on an interval size.
 Step 2: Make a frequency table.
 Step 3: Make a histogram to display the data.
Closure Question:
Which of the three data plots (stem, box, or dot) does not make it easy to find the mode?
Section 2-6
Warm – Up:
The table shows all the possible results of tossing two number cubes.
1. How many results are there?
2. a. List the results that have a sum of 1.
b. What is the probability of a sum of 1?
3. a. List the results that have a sum of 4.
b. What is the probability of a sum of 4?
4. a. List the results that have a sum of 11.
b. What is the probability of a sum of 11?
5. Find another sum that has the same probability of occurring as 11.
6. Are the sums 2 – 12 equally likely? Explain.
7. Are the probabilities of getting an even sum or an odd sum equal?
Objective: To find theoretical and experimental probability
probability: how likely it is that something will occur
outcome: the result of a single trial
sample space: all the possible outcomes
theoretical probability: probability based on outcomes that are equally likely
numberof  favorableoutcomes
P ( event )  
numberof  possibleoutcomes
Example #1:
a) A bowl contains 12 slips of paper, each with a different name of the month. Find the
theoretical probability that a slip selected at random has a name of the month that ends
with “ber.”
b) Suppose you write the names of days of the week on identical pieces of paper. Find the
theoretical probability of picking a piece of paper at random that has the name of a day
that starts with the letter “T.”
complement: all outcomes not in the event
P(event) + P(not event) = 1
or
P(not event) = 1- P(event)
Example #2:
a) On a popular television game show, a contestant must choose one of five envelopes. One
envelope contains the grand prize, a car. Find the probability of not choosing the car.
b) What happens to P(car) as the number of envelopes increases?
c) What happens to P(not car) as the number of envelopes increases?
odds: compares favorable outcomes to unfavorable outcomes
Example #3:
a) Find the odds in favor of the spinner landing on
a number greater than or equal to 6.
b) Find the odds against the spinner landing
on a number less than 3.
experimental probability: probability based on data collected from repeated trials
numberof timesaneventoccurs
P ( event ) 
numberof timestheexp erimentisdone
Example #4:
A bakery inspects a sample of 800 pastries and finds 12 that are defective.
a) What is the probability a pastry is defective?
b) The bakery altered the machinery, then inspected a new sample of 1500 and found 16
defective. Did the quality improve? Why?
Example #5:
A manufacturer inspects 700 light bulbs. She finds the probability that a light bulb works
is 99.7%. There are 35,400 light bulbs in the warehouse. Predict how many light bulbs
are likely to work.
Closure Question:
A spinner has 6 equal sections: 2 red, 2 blue, 2 green. Find the following:
a)
P(red)
b)
P(not red)
c)
odds of red
d)
odds against blue
Section 2-7
Warm – Up:
Suppose you roll a die with the numbers 1-10 on it. Find the following:
1) P(factor of 10)
2) P(not a factor of 10)
3) odds of a number less than 4
4) odds against rolling a 5
Simplify the following:
5)
2
14

7
6
6)
6
55

44
3
Objective: To find the probability of independent and dependent events
independent events: events that do not influence one another
(The occurrence of one event does not affect the probability of a second event.)
* Probability of Two Independent Events: P(A and B) = P(A)
P(B)
Example #1:
Suppose you roll two number cubes. What is the probability that you roll an odd number on
one cube and roll a 1 or 2 on the other cube?
Example #2:
Suppose you have 3 quarters and 5 dimes in your pocket. You take out one coin, and then
put it back. Then you take out another coin. What is the probability that you take out a
dime and then a quarter?
dependent events: events that influence each other
(The occurrence of one event affects the probability of a second event.)
* Probability of Two Dependent Events: P(A then B) = P(A)
P(B after A)
Example #3:
Suppose you have 3 quarters and 5 dimes in your pocket. You take out one coin from your
pocket. Without replacing the coin, you select a second coin. What is the probability of
first taking out a dime and then a quarter?
Example #4:
A teacher must select 2 students for a conference. The teacher randomly picks names from
among 3 freshman, 4 sophomores, 4 juniors, and 2 seniors. What is the probability that a
junior and then a senior are chosen?
Closure Question:
How does finding the probability of independent events compare to finding the probability
of dependent events?