Question

All but one of the following statements pertaining to the standard deviation of a distribution is...

All but one of the following statements pertaining to the standard deviation of a distribution is false. Select the option that is accurate.

a.

A dataset with the following observations (5, 7, 9, 11) will have the same standard deviation as a distribution with observations (4, 6, 8, 10).

b.

A dataset with the following observations (3, 5, 7, 9) would be unaffected were the following observations (1, 11) added to the distribution.

c.

When calculating population standard deviation, you lose one degrees of freedom because knowing n-1 of the deviations determines the last deviation.

d.

A distribution with a standard deviation of 47.5 would be described as more variable than a distribution with a standard deviation of 49.

Homework Answers

Answer #1

option A is correct because the difference between values in first data set is same as the difference between values in second data set and the number of data values is also same for both data set. So, standard deviations will also be same.

option B is false because adding 1 and 11 to the data set will change the standard deviation of the data set from 2.236 to 3.416. So, given statement is incorrect

option C is false because we use n-1 in case of sample standard deviation and n in case of population standard deviation

option D is false because higher standard deviation means higher variation. So, distribution with standard deviation 49 will be more variable as compared to that of the distribution with standard deviation of 47.5

answer is option A

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