Algebra 1:
Data Analysis Workday
STATION A
UNITOBJECTIVES:
1) a) I can represent data with plots on the real number line (dot plots, histograms, stem and leaf plots,
and box plots)
b) I can interpret data from these plots
2)a) I can calculate measures of center (median, mean) and spread (inter-quartile range)
b) I can use statistics appropriate to the shape of the data distribution to compare center (median, mean)
and spread (range, inter-quartile range)of two or more different sets.
3) a) I can determine whether or not a data set has an outlier.
b) I can interpret differences in shape, center, and spread in the context of the data sets, accounting for
possible effects of extreme data points (outliers).
#1. On a recent Precalculus quiz, Mr. Weiler found the
following distribution of scores, which are arranged in 5 point
intervals (with the exception of the last interval).
a) How many students scored at least 80 points?
b) Students do not pass the quiz if they receive lower than
a 70. How many students did not pass?
c) How many total students took the quiz?
d) Twenty-two students scored in the 80-84 range on this test. Does the histogram provide
us with enough information to conclude that a student must have scored an 82 on this
test? Explain your thinking.
e) Mr. Weiler assigned letter grades based on the scores, and he wants to know more about his letter
grade distribution. Give the percentage of the students taking the quiz who scored in each letter
grade interval. Show your work.
A: 90-100
B: 85-89
C: 75-84
D: 70-74
F: <70
Algebra 1:
Data Analysis Workday
STATION B
UNITOBJECTIVES:
1) a) I can represent data with plots on the real number line (dot plots, histograms, stem and leaf plots,
and box plots)
b) I can interpret data from these plots
2)a) I can calculate measures of center (median, mean) and spread (inter-quartile range)
b) I can use statistics appropriate to the shape of the data distribution to compare center (median, mean)
and spread (range, inter-quartile range)of two or more different sets.
3) a) I can determine whether or not a data set has an outlier.
b) I can interpret differences in shape, center, and spread in the context of the data sets, accounting for
possible effects of extreme data points (outliers).
#2. Charlie’s Food Factory currently employs 28
workers whose ages are shown on a dot plot.
How many of the workers are 18 years old?
What is the range of the ages of the workers?
Describe the shape of this distribution (symmetric vs. skewed, peaks, gaps, clusters, outliers). Be
specific!
Create a box and whisker plot for this data.
Min: _____
Q1: _______ Median: ____ Q3: ______ Max: _______
The mean age for a worker is 22 years old. Why is this average not representative of a typical worker?
What measure would you use instead? Defend your answer.
Are there any outliers? Justify mathematically!
Algebra 1:
Data Analysis Workday
STATION C
UNITOBJECTIVES:
1) a) I can represent data with plots on the real number line (dot plots, histograms, stem and leaf plots,
and box plots)
b) I can interpret data from these plots
2)a) I can calculate measures of center (median, mean) and spread (inter-quartile range)
b) I can use statistics appropriate to the shape of the data distribution to compare center (median, mean)
and spread (range, inter-quartile range)of two or more different sets.
3) a) I can determine whether or not a data set has an outlier.
b) I can interpret differences in shape, center, and spread in the context of the data sets, accounting for
possible effects of extreme data points (outliers).
#3. The speeds, in miles per hour, of 24 cars on a particular road are
recorded and represented on the box-and-whiskers diagram.
Find the range and IQR of the data set. Label each.
What is the maximum speed of the 24 drivers?
How many drivers drove between 30 and 42 miles per hour?
What percent of drivers drove at most 42 miles per hour?
If the speed limit on this part of the road is 35 miles per hour, are more people speeding or are more
people going the speed limit? Justify using the graph and measurements to prove your choice.
How SLOW does someone need to be driving to be considered an outlier to the data?
How FAST does someone need to be driving to be considered an outlier to the data?
Algebra 1:
Data Analysis Workday
STATION D
UNITOBJECTIVES:
1) a) I can represent data with plots on the real number line (dot plots, histograms, stem and leaf plots,
and box plots)
b) I can interpret data from these plots
2)a) I can calculate measures of center (median, mean) and spread (inter-quartile range)
b) I can use statistics appropriate to the shape of the data distribution to compare center (median, mean)
and spread (range, inter-quartile range)of two or more different sets.
3) a) I can determine whether or not a data set has an outlier.
b) I can interpret differences in shape, center, and spread in the context of the data sets, accounting for
possible effects of extreme data points (outliers).
#4. Calculate the five number summary and then draw a box plot for the stem and leaf plot.
Min: _____ Q1: _______ Median: ____ Q3: ______ Max: _______
Describe the distribution.
What is the IQR?
Are there any outliers in this data set? Justify algebraically.
Algebra 1:
Data Analysis Workday
STATION E
UNITOBJECTIVES:
1) a) I can represent data with plots on the real number line (dot plots, histograms, stem and leaf plots,
and box plots)
b) I can interpret data from these plots
2)a) I can calculate measures of center (median, mean) and spread (inter-quartile range)
b) I can use statistics appropriate to the shape of the data distribution to compare center (median, mean)
and spread (range, inter-quartile range)of two or more different sets.
3) a) I can determine whether or not a data set has an outlier.
b) I can interpret differences in shape, center, and spread in the context of the data sets, accounting for
possible effects of extreme data points (outliers).
#5. Part I: The mean age of 12 of the members attending a mathematics department faculty
meeting is 37 years old. Mr. Myers, who is 50 years old, arrives late. What is the average of all
13 members? Show your work!
Part II: If one of the teacher’s brings their 7 year old son to the meeting, how will this affect the
average age of the people there? Explain why this happened.
Part III: If one of the teacher’s brings their 95 year old granny to the meeting, how will this
affect the average age of the people there? Explain why this happened.
#6. Create one data set that reflects all of the following characteristics:
 The median of a set of 10 numbers is 24
 The range is 42
 To the nearest whole number, the mean is 24
 No more than three numbers are the same.
Show your strategy. Then prove your calculations work for each measurement!
Algebra 1:
Data Analysis Workday
STATION F
UNITOBJECTIVES:
1) a) I can represent data with plots on the real number line (dot plots, histograms, stem and leaf plots,
and box plots)
b) I can interpret data from these plots
2)a) I can calculate measures of center (median, mean) and spread (inter-quartile range)
b) I can use statistics appropriate to the shape of the data distribution to compare center (median, mean)
and spread (range, inter-quartile range)of two or more different sets.
3) a) I can determine whether or not a data set has an outlier.
b) I can interpret differences in shape, center, and spread in the context of the data sets, accounting for
possible effects of extreme data points (outliers).
#7. In 1961 Roger Maris made baseball headlines by hitting 61 homeruns, breaking a famous
record held by Babe Ruth. Here are Maris’ home run totals for his 10 seasons in the American
League. Would you consider his record- setting year to be an outlier?
8, 12, 14, 16, 23, 26, 28, 33, 39, 61
Calculate the mean and median of this data set.
Would you consider his record- setting year to be an outlier? Justify algebraically.
#8. A survey is taken by an insurance company to determine how
many car accidents the average New York City resident has gotten
into in the past 10 years. The company surveyed 20 people who are
getting off a train at a subway station. The following table gives the
results of the survey.
Calculate the mean and median number of accidents of this data set.
Are there any outliers in this data set? If so, what data value?
Justify algebraically (1.5 IQR’s away…).
Which number, the mean or median, better represents the number of accidents an average person
in this survey had over this 10 year period? Explain your answer.
Algebra 1:
Data Analysis Workday
STATION G
UNITOBJECTIVES:
1) a) I can represent data with plots on the real number line (dot plots, histograms, stem and leaf plots,
and box plots)
b) I can interpret data from these plots
2)a) I can calculate measures of center (median, mean) and spread (inter-quartile range)
b) I can use statistics appropriate to the shape of the data distribution to compare center (median, mean)
and spread (range, inter-quartile range)of two or more different sets.
3) a) I can determine whether or not a data set has an outlier.
b) I can interpret differences in shape, center, and spread in the context of the data sets, accounting for
possible effects of extreme data points (outliers).
#9. In Mr. Petrovic’s Algebra Course, eight students recently took a test. Their grades were as
follows:
45, 78, 82, 85, 87, 89, 93, 95
Calculate the mean and median of this data set.
Which score is an outlier? Justify algebraically.
Which measure of center is a better measure of how well the average student on Mr. Petrovic’s
quiz? Explain.
#10. A new coach has been working with the Long Jump team this month, and the athletes’
performance has changed. Augustus can now jump 0.15m further, June and Carol can jump
0.06m further.
The results for the entire Long Jump team are:
Augustus: +0.15m
Tom: +0.11m
June: +0.06m
Carol: + 0.06m
Bob: + 0.12m
Sam: - 0.56m
The head coach has to make a decision on whether or not to continue with the new coach. What
decision would you make? Justify your decision using the statistics we have discussed.
Algebra 1:
Data Analysis Workday
Opener – Data Representations
For the following sets of data, create a box-and-whisker plot using axes with the same scale.
Calculate the measures of center and measures of variability. Use the graph and these measures
to compare and contrast the data.
The number of stories in two selected samples of tall buildings in Atlanta and Philadelphia
55
63
60
50
52
26
70
40
47
53
32
29
Atlanta
44
36
44
34
52
32
32
28
34
32
40
38
32
31
50
61
58
54
53
50
Philadelphia
40
38
40
40
40
36
39
36
38
36
32
25
30
34
39
30
30
30
33
32
Create frequency table and histogram for the data. Label both axes and create even bins.