Standard Deviation Answers

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4

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Answer:

(5 - 4.9) / 2

5

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Answer:

(6.5 - 4.9) / 2

8

A set of data has a high-value outlier. How do you expect the standard deviation to change when the outlier is removed? Would the result be different if the data had a low-value outlier instead? Explain.

Answer:

The standard deviation will decrease when the outlier is removed. Standard deviation represents the spread of data from the mean. Both highvalue and lowvalue outliers increase the spread of a data set. Therefore, removing either a highvalue or a lowvalue outlier decreases the spread from the mean, which results in a lower standard deviation.

9

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11

Given that z = –2 and z = –1, which of the following do you know?

Question illustration
A
The variance is 10.
B
The standard deviation is 30.
C
The mean is 80.
D
The median is 40.
E
The data point x = 20 is 2 standard deviations from the mean.
F
The data point x = 50 is 1 standard deviation from the mean.
G
The data point x = 45 has a z-value of 1.5.
12

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14

Why does the formula use “n – 1” in the denominator?

A
The data is a sample and is expected to be more dispersed from the mean.
B
The data is a sample and is expected to be less dispersed from the mean.
C
The data is a population and is expected to be more dispersed from the mean.
D
The data is a population and is expected to be less dispersed from the mean.
15

Check each of the components below that you included in your response.

A
The standard deviation will decrease when the outlier is removed.
B
Standard deviation represents the spread of data from the mean.
C
Removing a high-value outlier decreases the spread of data from the mean.
D
Removing a low-value outlier decreases the spread of data from the mean.
E
In both cases the standard deviation decreases.
17

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18

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