a.
Find the
a.

Answer to Problem 13P
The range is 15.
Explanation of Solution
The range is obtained below:
Thus, the range is 15.
b.
Verify that
b.

Explanation of Solution
Step-by-step procedure to verify
- Press STAT.
- Select Edit.
- Enter the values in L1.
- Press STAT and Choose CALC.
- Select 1-Var Stats.
- To select the variable L1, Press 2-nd and then press 1.
- Press Enter.
Output obtained using the Ti83 calculator is given below:
From the output, the values of
c.
Find the sample variance and the sample standard deviation using the computation formula.
c.

Answer to Problem 13P
The sample variance using the computation formula is 37.
The sample standard deviation using the computation formula is 6.08.
Explanation of Solution
The sample variance using the computation formula is given below:
Where
The sample standard deviation using the computation formula is given below:
Where
The sample variance using the computation formula is obtained below:
Thus, the sample variance using the computation formula is 37.
The sample standard deviation using the computation formula is obtained below:
Thus, the sample standard deviation using the computation formula is 6.08.
d.
Find the sample variance using the defining formula.
Find the sample standard deviation using the defining formula.
d.

Answer to Problem 13P
The sample variance using the defining formula is 37.
The sample standard deviation using the defining formula is 6.08.
Explanation of Solution
The sample variance using the defining formula is given below:
Where
The sample standard deviation using the defining formula is given below:
Where
The value of
The value of
x | ||
23 | 1 | 1 |
17 | –5 | 25 |
15 | –7 | 49 |
30 | 8 | 64 |
25 | 3 | 9 |
The sample variance using the defining formula is given below:
Thus, the sample variance using the defining formula is 37.
The sample standard deviation using the defining formula is given below:
Thus, the sample standard deviation using the defining formula is 6.08.
e.
Find the population variance using the defining formula.
Find the population standard deviation using the defining formula.
e.

Answer to Problem 13P
The population variance using the defining formula is 29.6.
The population standard deviation using the defining formula is 5.44.
Explanation of Solution
The population variance using the defining formula is given below:
Where
The population standard deviation using the defining formula is given below:
Where
The value of
The value of
x | ||
23 | 1 | 1 |
17 | –5 | 25 |
15 | –7 | 49 |
30 | 8 | 64 |
25 | 3 | 9 |
The population variance using the defining formula is given below:
Thus, the population variance using the defining formula is 29.6.
The population standard deviation using the defining formula is given below:
Thus, the population standard deviation using the defining formula is 5.44.
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Chapter 3 Solutions
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