Standard Deviation Answers

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Which formula is used to calculate the standard deviation of sample data?

A
s = StartRoot StartFraction (x 1 minus x overbar) squared + (x 2 minus x overbar) squared + ellipsis + (x n minus x overbar) squared Over n minus 1 EndFraction EndRoot.
Option A
B
sigma squared = StartFraction (x 1 minus mu) squared + (x 2 minus mu) squared + ellipsis + (x N minus mu) squared Over N EndFraction
Option B
C
Sigma = StartRoot StartFraction (x 1 minus mu) squared + (x 2 minus mu) squared + ellipsis + (x N minus mu) squared Over N EndFraction EndRoot
Option C
D
x = StartFraction (x 1 minus x overbar) squared + (x 2 minus x overbar) squared + ellipsis + (x n minus x overbar) squared Over n minus 1 EndFraction
Option D
3

Yuri computes the mean and standard deviation for the sample data set 12, 14, 9, and 21. He finds the mean is 14. His steps for finding the standard deviation are below.What is the first error he made in computing the standard deviation?

Question illustration
A
Yuri failed to find the difference between each data point and the mean.
B
Yuri divided by n instead of n -1.
C
Yuri did not subtract 9 - 14 correctly.
D
Yuri failed to square -2 correctly.
5

Fiona recorded the number of miles she biked each day last week as shown below.4, 7, 4, 10, 5The mean is given by m = 6. Which equation shows the variance for the number of miles Fiona biked last week?

A
s squared = StartFraction (4 minus 6) squared + (7 minus 6) squared + (4 minus 6) squared + (10 minus 6) squared + (5 minus 6) squared Over 6 EndFraction
Option A
B
Sigma = StartRoot StartFraction (4 minus 6) squared + (7 minus 6) squared + (4 minus 6) squared + (10 minus 6) squared + (5 minus 6) squared Over 5 EndFraction EndRoot
Option B
C
s = StartRoot StartFraction (4 minus 6) squared + (7 minus 6) squared + (4 minus 6) squared + (10 minus 6) squared + (5 minus 6) squared Over 4 EndFraction EndRoot
Option C
D
Sigma squared = StartFraction (4 minus 6) squared + (7 minus 6) squared + (4 minus 6) squared + (10 minus 6) squared + (5 minus 6) squared Over 5 EndFraction
Option D
7

Abby is collecting rainfall data. She finds that one value of the data set is a high-value outlier. Which statement must be true?

A
Abby will use a different formula for calculating the standard deviation.
B
The outlier will increase the standard deviation of the data set.
C
The spread of the graph of the data will not change.
D
Abby will not use the mean when calculating the standard deviation.
10

The monthly mean salaries and standard deviations of four college students are given below.StudentMeanStandard DeviationClarissa$34512.53Abi$5988.99Kaila$81215.29Shenika$2087.67Which statement must be true?

A
The monthly salary of Shenika is less spread out than the monthly salary of Clarissa.
B
The monthly salary of Kaila is less spread out than the monthly salary of Abi.
C
The monthly salary of Abi is less spread out than the monthly salary of Shenika.
D
The monthly salary of Clarissa is less spread out than the monthly salary of Abi.

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