Question

Each of the following three data sets represents the IQ scores of a random sample of adults. IQ scores are known to have a mean and median of 100. For each data​ set, determine the sample standard deviation. Then recompute the sample standard deviation assuming that the individual whose IQ is

108 is accidentally recorded as 180. For each sample​ size, state what happens to the standard deviation. Comment on the role that the number of observations plays in resistance.

Sample of Size 5
105	110	96	97	118

Sample of Size 12
105	110	96	97	118	93
94	103	96	106	107	117

Sample of Size 30
105	110	96	97	118	93
94	103	96	106	107	117
111	112	94	108	96	103
101	93	91	113	118	96
103	117	102	117	109	113

For each data​ set, compute the standard deviation.

What is the standard deviation of the sample of size​ 5?

​(Type an integer or decimal rounded to one decimal place as​ needed.)

What is the standard deviation of the sample of size​ 12?

​(Type an integer or decimal rounded to one decimal place as​ needed.)

What is the standard deviation of the sample of size​ 30?

​(Type an integer or decimal rounded to one decimal place as​ needed.)

For each data set recalculate the standard​ deviation, assuming that the individual whose IQ is

108 is accidently recorded as 180.

What is the standard deviation of the new sample of size​ 5?

​(Type an integer or decimal rounded to one decimal place as​ needed.)

What is the standard deviation of the new sample of size​ 12?

​(Type an integer or decimal rounded to one decimal place as​ needed.)

What is the standard deviation of the new sample of size​ 30?

​(Type an integer or decimal rounded to one decimal place as​ needed.)

For each sample​ size, the standard deviation______?  increased, decreased or remained constant?

Comment on the role that the number of observations plays in resistance.

A.

As the sample size​ increases, the impact of the misrecorded data on the standard deviation decreases.

B.

As the sample size​ increases, the impact of the misrecorded data on the standard deviation remains the same.

C.

As the sample size​ increases, the impact of the misrecorded data on the standard deviation increases.

Answer 1

The standard deviation of the sample of size​ 5=9.2

The standard deviation of the sample of size​ 12=8.6

The standard deviation of the sample of size​ 30=8.7

Since in the samples of size 5 and size 12, there are no such individual whose IQ is 108, so the standard deviations of sample sizes 5 and 12 remain same.

Now for sample of size 30, the standard deviation of the new sample of size​ 30=16.3

For each sample​ size, the standard deviation increased.

For answering the last part, we consider three samples are as follows:

n=5:

111

112

94

108

96

103

n=12

94	103	96	106	107	117
111	112	94	108	96	103

n=30

105	110	96	97	118	93
94	103	96	106	107	117
111	112	94	108	96	103
101	93	91	113	118	96
103	117	102	117	109	113

The standard deviation of the sample of size​ 5=7.7

The standard deviation of the sample of size​ 12=7.6

The standard deviation of the sample of size​ 30=8.7

Now 108 is accidentally recorded as 180 then

The standard deviation of the new sample of size​ 5=32.2

The standard deviation of the new sample of size​ 12=23.3

The standard deviation of the new sample of size​ 30=16.3

Hence Option:

A. As the sample size​ increases, the impact of the misrecorded data on the standard deviation decreases.