$$L = \frac{25}{100} \times 20 = 5$$

$$Q_1 - 1.5$$ \times IQR = 46 - 1.5 \times 6 = 37$$

Question 1

Which of the following statements about Z-scores is TRUE?

Accepted Answer

A Z-score represents the number of standard deviations a data value is from the mean.

Question 2

Given a sample with mean $$\mu = 50$$ and standard deviation $$\sigma = 8$$, what is the Z-score for a value of $$62$$?

Accepted Answer

$$Z = \frac{62 - 50}{8} = 1.50$$

Question 3

A student scores 88 on a test where the mean is 80 and the standard deviation is 4. What is the student's Z-score?

Accepted Answer

$$Z = \frac{88 - 80}{4} = 2.00$$

Question 4

Which value is considered 'unusual' based on Z-scores?

Accepted Answer

A value with $$|Z| \u003e 2$$

Question 5

If a data value is smaller than the mean, what can you say about its Z-score?

Accepted Answer

The Z-score will be negative.

Question 6

How do you calculate the location $$L of $$the value that cuts off the bottom $$k$$ percent of data in a set of $$n$$ values?

Accepted Answer

$$L = \frac{k}{100} 	imes n$$

Question 7

In a data set of 20 values, what is the location of the value that cuts off the bottom 25% of the data?

Accepted Answer

$$L = \frac{25}{100} 	imes 20 = 5$$

Question 8

Which of the following best describes the first quartile $$Q_1$$?

Accepted Answer

It separates the bottom 25% of data from the top 75%.

Question 9

What is the formula for the interquartile range (IQR)?

Accepted Answer

$$IQR = Q_3$ - Q_1$

Question 10

A boxplot is constructed using which summary statistics?

Accepted Answer

Minimum, $$Q_1$$, Median, $$Q_3$$, Maximum

Question 11

Given $$Q_1 = 46$, Q_3$ = 52$$, and $$IQR = 6$$, what is the lower outlier threshold?

Accepted Answer

$$Q_1 - 1.5$$ 	imes IQR = 46 - 1.5 	imes 6 = 37$$

Question 12

Which value from the following data set is an outlier: $$20, 39, 45, 46, 47, 49, 50, 52, 53, 54, 58$$?

Accepted Answer

20

Question 13

Which of the following is NOT a property of percentiles?

Accepted Answer

Percentiles are the same as quartiles.

Question 14

If the 88th percentile in a data set of 15 values is located at $$L = 13.2$$, which value do you use for the percentile?

Accepted Answer

The 13th value in the ordered data set.

Question 15

Which of the following statements about boxplots is FALSE?

Accepted Answer

Boxplots use the mean and standard deviation to display data.

Question 16

A value in a data set has a Z-score of $$-3.10. $$What does this indicate?

Accepted Answer

The value is unusually low compared to the mean.

Question 17

Which of the following is the correct formula for calculating a Z-score from population data?

Accepted Answer

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

Question 18

Which of the following best describes the median?

Accepted Answer

It is the value that separates the bottom 50% of data from the top 50%.

Measures of Relative Standing: Z-Scores, Percentiles, Quartiles, and Boxplots

Study Guide - Practice Questions