Download Exercises for Section 2.3

Exercises for Section 2.3 (Measures of Center and Spread)
Statistics
(questions correspond to those from pages 71 – 74 of the text. For some you will
need to consult the text for the diagrams referred to).
E29.) The mean of a set of seven values is 25. Six of the values are 24, 47, 34, 10,
22, and 28. What is the 7th value?
E30.) The sum of a set of values is 84, and the mean is 6. How many values are
there?
E31.) Three histograms and three boxplots appear in Display 2.58. Which boxplot
displays the same information as:
a.) histogram A? _________
b.) histogram B? _________
c.) histogram C? _________
E32.) The test scores of 40 students in a first period class were used to construct
the first boxplot in Display 2.59, and the test scores of 40 students in a
second-period class were use cot construct the second. Can the third plot be
a boxplot of the combined scores of the 80 students in the two classes? Why
or why not?
E33.) Make side-by-side boxplots of the speeds of predators and nonpredators.
(The stemplot in Display 2.31 on page 48 shows the values ordered.)
(construct the two boxplots above the number line).
0
10
20
30
40
50
60
70
80
Are the boxplots or the back-to-back stemplot in Display 2.3 better for
comparing these speeds? Explain.
E36.) The boxplots in this exercise show the average longevity of mammals, from
Display 2.24.
a.) Using only the basic boxplot in Display 2.60, show that there must be at
least one outlier in the set of average longevity.
b.) How many outliers are there in the modified boxplot of average
longevity in Display 2.61?
c.) How many outliers are shown in Display 2.49 on page 62? How can that
be, considering the boxplot in Display 2.61?
E37.) No computing should be necessary to answer these questions.
a.) The mean of each of these sets of values is 20, and the range is 40.
I.
II.
III.
0 10 20 30 40
0 0 20 40 40
0 19 20 21 40
Which set has the largest standard deviation?
Which has the smallest?
b.) Two of these sets of values have a standard deviation of about 5.
I. 5 5 5 5 5 5
II. 10 10 10 20 20 20
III. 6 8 10 12 14 16 18 20 22
IV. 5 10 15 20 25 30 35 40 45
Which two have a standard deviation of about 5?
E38.) The standard deviation of the first set of values listed here is about 32.
What is the standard deviation of the second set? Explain. (No computing
should be necessary.)
16 23 34 56 78 92 93
20 27 38 60 82 96 97
E39.) Consider the set of the heights of all female National Collegiate Athletic
Association (NCAA) athletes and the set of the heights of all female NCAA
basketball players.
a.) Which distribution will have the larger mean?
b.) Which will have the larger standard deviation? Explain.
E43.) This table shows the weights of 100 pennies.
Weight Frequency
2.99
1
3.01
4
3.03
4
3.05
4
3.07
7
3.09
17
3.11
24
3.13
17
3.15
13
3.17
6
3.19
2
3.21
1
a.) Find the mean weight of the pennies.
b.) Find the standard deviation.
c.) Does the standard deviation appear to represent a typical deviation from
the mean?
E45.) On the first test of the semester, the scores of the first-period class of 30
students had a mean of 75 and a median of 70. The scores of the secondperiod class of 22 students had a mean of 70 and a median of 68.
a.) To the nearest tenth, what is the mean test score of all 52 students? If
you cannot calculate the mean of the two classes combined, explain
why.
b.) What is the median test score of all 52 students? If you cannot find the
median of the two classes combined, explain why.