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Chapter 3: Problem 87

Construct two sets of numbers with at least five numbers in each set with the following characteristics: The means are different, but the standard deviations are the same. Report the standard deviation and both means.

Short Answer

Expert verified
The first set of numbers: 2, 4, 6, 8, 10 with the mean of 6 and standard deviation of 2.83. The second set of numbers: 1, 3, 5, 7, 9 with the mean of 5 and the same standard deviation of 2.83.

Step by step solution

01

Define the first set.

Choose five numbers, let's say: 2, 4, 6, 8, 10. Calculate the mean and standard deviation. The mean, often called the average, is 6. The standard deviation is approximately 2.83.
02

Create another set with the same standard deviation, but a different mean.

Adjust the numbers initially chosen in a way that the standard deviation remains the same, but the mean changes. Let's create the second set as: 1, 3, 5, 7, 9. The mean becomes 5 and standard deviation is the same as in the first set.
03

Verify the values

To make sure that the calculations were made correctly, it's essential to check if the standards deviation are the same in both sets, and if the means are different. In this case, confirm that the mean for the first set is indeed 6 and for the second set it's 5. And the standard deviation for both sets is 2.83.

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