Concept explainers
a.
To sketch: A box-and-whisker of the number of women’s teams playing a sport.
a.
Answer to Problem 24E
The standard deviation is
Explanation of Solution
Given information:
The number of times the first 42 presidents vetoed bills are listed.
Graph:
Interpretation:
Variability of the data can be studied by box-and-whisker plot. The box-and-whisker plot represent the data of the number of vetos. The median of the data is 29.
b.
To calculate: The mean deviation of the data.
b.
Answer to Problem 24E
The mean deviation is
Explanation of Solution
Given information:
The number of times the first 42 presidents vetoed bills are listed.
Formula used:
The arithmetic mean of the absolute values of the deviations from the mean of a set of data is called the mean deviation.
Formula of Mean
Calculation:
Consider the data in ascending order ,
So,
The mean of the data is
The mean deviation is −
2 | 60.4 | |
0 | 60.4 | |
0 | 60.4 | |
7 | 60.4 | |
1 | 60.4 | |
0 | 60.4 | |
12 | 60.4 | |
1 | 60.4 | |
0 | 60.4 | |
10 | 60.4 | |
3 | 60.4 | |
0 | 60.4 | |
0 | 60.4 | |
9 | 60.4 | |
7 | 60.4 | |
6 | 60.4 | |
29 | 60.4 | |
93 | 60.4 | |
13 | 60.4 | |
0 | 60.4 | |
12 | 60.4 | |
414 | 60.4 | |
44 | 60.4 | |
170 | 60.4 | |
42 | 60.4 | |
82 | 60.4 | |
39 | 60.4 | |
44 | 60.4 | |
6 | 60.4 | |
50 | 60.4 | |
37 | 60.4 | |
635 | 60.4 | |
250 | 60.4 | |
181 | 60.4 | |
21 | 60.4 | |
30 | 60.4 | |
43 | 60.4 | |
66 | 60.4 | |
31 | 60.4 | |
78 | 60.4 | |
44 | 60.4 | |
25 | 60.4 | |
Hence, the mean deviation is
c.
To calculate: The variance of the data.
c.
Answer to Problem 24E
The variance is
Explanation of Solution
Given information:
The number of times the first 42 presidents vetoed bills are listed.
Formula used:
A measure of variability associated with the arithmetic mean is the standard deviation.
The variance is the mean of the squares of the deviations from
The standard deviation is the positive square root of the variance.
Calculation:
Consider the data in ascending order ,
So,
The mean of the data is
The standard deviation is −
2 | 60.4 | ||
0 | 60.4 | ||
0 | 60.4 | ||
7 | 60.4 | ||
1 | 60.4 | ||
0 | 60.4 | ||
12 | 60.4 | ||
1 | 60.4 | ||
0 | 60.4 | ||
10 | 60.4 | ||
3 | 60.4 | ||
0 | 60.4 | ||
0 | 60.4 | ||
9 | 60.4 | ||
7 | 60.4 | ||
6 | 60.4 | ||
29 | 60.4 | ||
93 | 60.4 | ||
13 | 60.4 | ||
0 | 60.4 | ||
12 | 60.4 | ||
414 | 60.4 | ||
44 | 60.4 | ||
170 | 60.4 | ||
42 | 60.4 | ||
82 | 60.4 | ||
39 | 60.4 | ||
44 | 60.4 | ||
6 | 60.4 | ||
50 | 60.4 | ||
37 | 60.4 | ||
635 | 60.4 | ||
250 | 60.4 | ||
181 | 60.4 | ||
21 | 60.4 | ||
30 | 60.4 | ||
43 | 60.4 | ||
66 | 60.4 | ||
31 | 60.4 | ||
78 | 60.4 | ||
44 | 60.4 | ||
25 | 60.4 | ||
Hence, the variance is
d.
To calculate: The standard deviation of the data.
d.
Answer to Problem 24E
The standard deviation is
Explanation of Solution
Given information:
The number of times the first 42 presidents vetoed bills are listed.
Formula used:
A measure of variability associated with the arithmetic mean is the standard deviation.
Formula of Mean
Calculation:
Consider the data in ascending order ,
So,
The mean of the data is
The standard deviation is −
2 | 60.4 | ||
0 | 60.4 | ||
0 | 60.4 | ||
7 | 60.4 | ||
1 | 60.4 | ||
0 | 60.4 | ||
12 | 60.4 | ||
1 | 60.4 | ||
0 | 60.4 | ||
10 | 60.4 | ||
3 | 60.4 | ||
0 | 60.4 | ||
0 | 60.4 | ||
9 | 60.4 | ||
7 | 60.4 | ||
6 | 60.4 | ||
29 | 60.4 | ||
93 | 60.4 | ||
13 | 60.4 | ||
0 | 60.4 | ||
12 | 60.4 | ||
414 | 60.4 | ||
44 | 60.4 | ||
170 | 60.4 | ||
42 | 60.4 | ||
82 | 60.4 | ||
39 | 60.4 | ||
44 | 60.4 | ||
6 | 60.4 | ||
50 | 60.4 | ||
37 | 60.4 | ||
635 | 60.4 | ||
250 | 60.4 | ||
181 | 60.4 | ||
21 | 60.4 | ||
30 | 60.4 | ||
43 | 60.4 | ||
66 | 60.4 | ||
31 | 60.4 | ||
78 | 60.4 | ||
44 | 60.4 | ||
25 | 60.4 | ||
Hence, the standard deviation is
e.
To discuss: The variability of the data.
e.
Answer to Problem 24E
The standard deviation is
Explanation of Solution
Given information:
During a season, 7684n teams played 19 NCAA women’s sports.
Formula used:
Median for even terms =
Median for odd terms =
Calculation:
Consider the data in ascending order ,
Since there are seven rivers. So,
There is odd number of data.
The median of odd number of data is −
Hence, the median is
Chapter 14 Solutions
Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
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