Question 1

Which of the following is the best definition of the mean of a data set?

Accepted Answer

The sum of all values divided by the number of values.

Question 2

Given the data set: 2, 4, 4, 6, 8, what is the mode?

Accepted Answer

4

Question 3

Which measure of center is most affected by an extreme value (outlier)?

Accepted Answer

Mean

Question 4

A sample of exam scores is: 70, 75, 80, 85, 90. What is the median?

Accepted Answer

80

Question 5

Which formula correctly calculates the sample mean $\bar{x}$ for $n$ values $x_1, x_2, ..., x_n$?

Accepted Answer

$\bar{x} = \dfrac{\sum_{i=1}^n x_i}{n}$

Question 6

If a data set is skewed right, which measure of center is typically greater?

Accepted Answer

Mean

Question 7

What is the range of the following data set: 3, 7, 8, 10, 15?

Accepted Answer

12

Question 8

Which formula is used to calculate the sample standard deviation $s$?

Accepted Answer

$s = \sqrt{\dfrac{\sum_{i=1}^n (x_i - \bar{x})^2}{n-1}}$

Question 9

A data set has a mean of 50 and a standard deviation of 5. What is the z-score for a value of 60?

Accepted Answer

$z = 2$

Question 10

Which of the following statements about the Empirical Rule is correct?

Accepted Answer

About 68% of data falls within one standard deviation of the mean in a bell-shaped distribution.

Question 11

Which of the following is NOT a measure of variation?

Accepted Answer

Median

Question 12

Given the data set: 2, 4, 6, 8, 10, what is the interquartile range (IQR)?

Accepted Answer

4

Question 13

Which of the following best describes the five-number summary?

Accepted Answer

Minimum, Q1, Median, Q3, Maximum

Question 14

A boxplot is useful for displaying which of the following?

Accepted Answer

The five-number summary and potential outliers

Question 15

If all values in a data set are increased by 5, what happens to the standard deviation?

Accepted Answer

It remains the same

Question 16

Which of the following is the correct formula for the z-score of a value $x$ in a data set with mean $\mu$ and standard deviation $\sigma$?

Accepted Answer

$z = \dfrac{x - \mu}{\sigma}$

Question 17

Which scenario best illustrates when the median is a better measure of center than the mean?

Accepted Answer

A data set with a significant outlier

Question 18

If the variance of a data set is 16, what is the standard deviation?

Accepted Answer

4

Question 19

Which of the following is true about the mode?

Accepted Answer

A data set can have more than one mode.

Question 20

A company wants to compare the consistency of two machines. Machine A has a standard deviation of 2, and Machine B has a standard deviation of 5. Which machine is more consistent?

Accepted Answer

Machine A

Descriptive Measures in Statistics: Measures of Center, Variation, and Position

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