Math 116 – Take Home Exam 1 – Chapters 1, 2, 3, 4, 5 – Spring 2011 Name__________________
I would prefer you work on your own without help from other students; just you and your book.
All questions on this page refer to the same story
1) We asked the question: “How many TV sets do you have?” to two groups of students.
The answers were anywhere from 0 to 4. The results obtained are shown by the two frequency histograms
shown below.
On the horizontal axes, label the bars of each histogram with the numbers 0, 1, 2, 3, 4
DISTRIBUTION A
DISTRIBUTION B
Part 1: Look at the histograms, think and answer by selecting the correct choice:
a) In comparing the means of both distributions, which of the following statements is correct? Circle one
1) Distribution A has a larger mean
2) Distribution B has a larger mean
3) Both distributions have the same mean
4) We can’t tell without the data
b) In comparing the standard deviations of both distributions, which of the following is correct? Circle one
1) Distribution A has a larger standard deviation
2) Distribution B has a larger standard deviation
3) Both distributions have the same standard deviation
4) We can’t tell without the data
c) In comparing the ranges of both distributions, which of the following is correct? Circle one
1) Distribution A has a larger range
2) Distribution B has a larger range
3) Both distributions have the same range
4) We can’t tell without the data
Part 2: Make up a possible set of values for the DISTRIBUTION A
Part 3: Make up a possible set of values for the DISTRIBUTION B
2) All questions on this page are related to the box-plots shown below
Data set I
Data Set II
10 20 30 40 50 60 70 80
909090
9090
Part I – Complete the following:
a) The minimum value of data set II is __________
b) The range of data set I is ___________________
(Show how you find it)
c) The median of data set I is __________
d) The interquartile range of data set II is _____________ (Show how you find it)
e) The third quartile of data set I is ________
f) The first quartile of data set II is _______
g) List the five-number-summary for data set I __________________________________
Part II – Circle the correct choice:
a) TRUE OR FALSE? In data set I there are more data values between the first quartile and the median than
between the median and the third quartile.
b) TRUE OR FALSE? About 75% of the values in data set I are smaller than or equal to about 75% of the
values in data set II.
c) Circle the choice that describes the shape of the distribution
DATA SET I
Left Skewed
Close to Symmetric
Right Skewed
DATA SET II
Left Skewed
Close to Symmetric
Right Skewed
3) Babe Ruth played 15 years with the Yankees. Here are the number of home runs he hit in each of those
seasons:
54
59 35
41
46
25
47 60
54
46
49
46
41
34
22
In 2001 Barry Bonds broke the record again with 73 home runs. Here are his totals for the 20 years he has
been in professional baseball.
16
25
24
19
33
25
34
46
37
33
42
40
37
34
49
73
46
45
45
5
a) Construct a back-to-back stem and leaf plot for both baseball players. It does not have to be in order.
b) Based on the stem plot, who is a better home run hitter? How did the graph help you in answering the
question?
c) Enter the data in the calculator and construct parallel box plots. Transfer them below using the provided scale
d) Based on the box plots, who is a better home run hitter? How did the graph help you in answering the
question? Use the scale provided at the bottom of the page to draw the box plots.
Organize the neat work below and label parts (a) – (d)
___|_____|_____|_____|_____|_____|_____|_____|_____|_____|_____|_____|_____|_____|_____|_____|__
5
10
15
20
4) Follow directions, please!
a) Create a list of 5 different numbers with a median of 10
b) Create a list of 4 different numbers with a median of 10
c) Create a list of 4 different numbers with a mean of 10
d) Create a list of 8 numbers with a range of 10
e) Create a list of 5 numbers with a standard deviation of zero. The numbers should not be zero.
5) A mine foreman is comparing the products of two manufacturers of blasting materials. Both companies’
materials explode a mean time of 40 minutes after they are set off, but the standard deviation for KaBoom
brand materials is 4 minutes and the standard deviation for It’s-a-Blast brand materials is 14 minutes.
Which brand should he choose? Must show work to explain your reasoning
6) John and Bob are salesmen in different districts. In John’s district his long term average sales are
$17,319 each month with a Stddev of $684. In Bob’s district, his long term average sales are $21,971
each month with a Stddev of $495. Each of the districts sales are normally distributed.
Last month John sold $19,214 and Bob sold $22,718 in their respective districts. Whose sales are
“better”? Support your answer with appropriate calculations and drawings. Draw and label.