
a.
To choose: Four numbers that have the smallest possible standard deviation.
a.

Answer to Problem 2.39E
The four numbers chosen would have same values to get the smallest standard deviation.
Explanation of Solution
Given info:
From the whole numbers 0 to 10, four numbers are chosen with repetition.
Justification:
Standard deviation:
Formula for standard deviation is,
Standard deviation is always zero or greater than zero. If the observations have the same value with no variability then the standard deviation is zero. The standard deviation increases as the variability increases.
For example, the sets
Thus, the four number set with the same values have the smallest possible standard deviation.
b.
To choose: Four numbers that have the largest possible standard deviation.
b.

Answer to Problem 2.39E
The four numbers that have the largest standard deviation is
Explanation of Solution
Calculation:
Suppose a set of four numbers
Mean:
The
Formula for mean is:
The
Thus, the mean is 5.
Standard deviation:
Formula for standard deviation is:
The standard deviation for the set
Thus, the standard deviation is 5.77.
Suppose a set of four numbers
Mean:
The sample size n is 4.
Formula for mean is:
The mean value for the set
Thus, the mean is 7.5.
Standard deviation:
Formula for standard deviation is:
The standard deviation for the set
Thus, the standard deviation is 5.
From the whole numbers 0 to 10, the set
Thus, the four numbers that have the largest standard deviation is
c.
To check: Whether more than one choice is possible in either part (a) or part (b).
c.

Answer to Problem 2.39E
More than one choice is possible in part (a) but not in part (b).
Explanation of Solution
From part (a), the least possible standard deviation is 0. Since, the whole numbers 0 to 10 can be repeatedly taken in a set of four numbers; there is more than one choice possible in part (a). But in part (b), the highest standard deviation is found and there is only one way to get using the whole numbers from 0 to 10 with repetition.
Thus, more than one choice is possible in part (a).
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Chapter 2 Solutions
EBK THE BASIC PRACTICE OF STATISTICS
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