Q: What is the formula for the range of a data set?

$$\text{Range} = \text{Maximum} - \text{Minimum}$$

Question 1

Which measure of center is most affected by extreme values in a data set?

Accepted Answer

Mean

Question 2

Given the data set: 4, 5, 5, 7, 9, what is the median?

Accepted Answer

5

Question 3

Which formula correctly calculates the sample variance $$s^2$$ for a data set $$x_1$$, $$x_2$$, ..., x_n$$ with mean $$\bar{x}$$?

Accepted Answer

$$s^2$$ = \frac{\sum (x_i - \bar{x}$$)^2$$}{n-1}$$

Question 4

A supermarket checkout line has the following frequency distribution for time spent (in minutes): 0-4 (5 customers), 5-9 (8 customers), 10-14 (7 customers). What is the mean checkout time using midpoints?

Accepted Answer

7.5 minutes

Question 5

Which measure of center is most appropriate for nominal data?

Accepted Answer

Mode

Question 6

If a data set is normally distributed with mean $$\mu$$ and standard deviation $$\sigma$$, what percent of data falls within one standard deviation of the mean according to the Empirical Rule?

Accepted Answer

68%

Question 7

A baby at a hospital weighs 6.8 pounds. The mean birth weight is 8 pounds with a standard deviation of 0.4 pounds. What is the z-score for this baby’s weight?

Accepted Answer

$$z = \frac{6.8 - 8}{0.4} = -3$$

Question 8

Which of the following is NOT a property of the standard deviation?

Accepted Answer

It decreases as data values become more spread out

Question 9

For the data set 2, 5, 8, 10, what is the midrange?

Accepted Answer

6

Question 10

Which of the following best describes the purpose of a boxplot?

Accepted Answer

To visually compare data sets using the same scale and show spread and outliers

Question 11

If a value is more than two standard deviations above the mean, how is it classified according to the Range Rule of Thumb?

Accepted Answer

Significantly high

Question 12

Which formula is used to calculate a z-score for a data value $$x$$ with mean $$\mu$$ and standard deviation $$\sigma$$?

Accepted Answer

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

Question 13

Which measure of variation is most sensitive to extreme values?

Accepted Answer

Range

Question 14

A data set has the values 2, 4, 6, 8, 10. What is the sample mean?

Accepted Answer

6

Question 15

Which of the following is a disadvantage of using the median as a measure of center?

Accepted Answer

It does not take all data values into account

Question 16

What is the main advantage of using the standard deviation over the range as a measure of variation?

Accepted Answer

Standard deviation uses all data values and is less affected by outliers

Question 17

If a data set is skewed right, which measure of center is likely to be greater than the others?

Accepted Answer

Mean

Question 18

Which of the following is NOT true about percentiles?

Accepted Answer

Percentiles are only used for nominal data

Question 19

What is the formula for the range of a data set?

Accepted Answer

$$	ext{Range} = 	ext{Maximum} - 	ext{Minimum}$$

Question 20

Which step is NOT part of constructing a boxplot?

Accepted Answer

Find the mean of the data

Describing, Exploring, and Comparing Data: Measures of Center, Variation, and Relative Standing

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