Q: If a data set has $$n = 50$$ values and you want to find the value at the 25th percentile ($$P_{25}$$), what is the locator $$L$$ and which value do you use?

$$L = 0.25 \times 50 = 12.5$$, use the 13th value

Q: Which of the following best describes the process for finding the percentile of a data value $$x in a $$sorted data set of size $$n$$?

Percentile = $$\frac{\text{number of values less than } x}{n} \times 100$$

Q: A data set has $$Q_1 = 20$, Q_3$ = 40. $$What is the range of values that are NOT considered outliers?

$$[20 - 1.5 \times 20, 40 + 1.5 \times 20] = [-10, 70]$$

Question 1

A z score is calculated for a value $$x in a $$data set with mean $$\mu = 50$$ and standard deviation $$\sigma = 8. If$$ $$x = 66$$, what is the z score for this value?

Accepted Answer

$$z = \frac{66 - 50}{8} = 2.00$$

Question 2

Which of the following statements about z scores is TRUE?

Accepted Answer

A z score is the number of standard deviations a value is above or below the mean.

Question 3

A data value has a z score of $$-2.5. $$According to the rules for significant values, how would you classify this value?

Accepted Answer

Significantly low

Question 4

A set of earthquake magnitudes has a mean of $$2.572$$ and a standard deviation of $$0.651. Is a $$magnitude of $$4.01$$ significantly high?

Accepted Answer

Yes, because $$z = \frac{4.01 - 2.572}{0.651} = 2.21$$, which is significantly high.

Question 5

Which of the following best describes the 5-number summary of a data set?

Accepted Answer

Minimum, Q1, median, Q3, maximum

Question 6

Given the following 5-number summary for wait times (in minutes): 10, 25, 35, 50, 110. What is the interquartile range (IQR)?

Accepted Answer

$$IQR = Q3 - Q1 = 50 - 25 = 25$$

Question 7

If a data set has $$n = 50$$ values and you want to find the value at the 25th percentile ($$P_{25}$$), what is the locator $$L$$ and which value do you use?

Accepted Answer

$$L = 0.25 	imes 50 = 12.5$$, use the 13th value

Question 8

Which of the following is TRUE about quartiles?

Accepted Answer

$$Q_2 is $$the same as the median.

Question 9

A boxplot is constructed for a data set. Which of the following features would indicate that the data is right-skewed?

Accepted Answer

The median is closer to $$Q_3$$ and the right whisker is longer.

Question 10

Given $$Q_1 = 25$, Q_3$ = 50$$, and $$IQR = 25$$, which value would be considered an outlier in a modified boxplot?

Accepted Answer

A value of 110

Question 11

Which of the following best describes the process for finding the percentile of a data value $$x in a $$sorted data set of size $$n$$?

Accepted Answer

Percentile = $$\frac{	ext{number of values less than } x}{n} 	imes 100$$

Question 12

A data set has $$Q_1 = 20$, Q_3$ = 40. $$What is the range of values that are NOT considered outliers?

Accepted Answer

$$[20 - 1.5 	imes 20, 40 + 1.5 	imes 20] = [-10, 70]$$

Question 13

Which of the following is NOT part of the 5-number summary?

Accepted Answer

Mean

Question 14

If a value has a z score of $$1.8$$, how would you interpret this value?

Accepted Answer

It is not significant.

Question 15

Which of the following is a correct interpretation of the 72nd percentile for a wait time of 45 minutes?

Accepted Answer

72% of wait times are less than 45 minutes.

Question 16

Which of the following is TRUE about modified boxplots?

Accepted Answer

They use a special symbol to identify outliers.

Measures of Relative Standing and Boxplots: Describing, Exploring, and Comparing Data

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