Q: Which of the following is a correct method for identifying outliers using the interquartile range (IQR)?

A value is an outlier if it is below $$Q_1 - 1.5$$ \times IQR$$ or above Q_3$ + 1.5 \times IQR.$$

Q: A data set has $$Q_1 = 7.9$, Q_3$ = 21.5. $$What is the range of values that are NOT considered outliers?

$$[7.9 - 1.5 \times (21.5 - 7.9),\ 21.5 + 1.5 \times (21.5 - 7.9)]$$

Question 1

Which of the following best describes a z score?

Accepted Answer

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

Question 2

Given a sample with mean $$\overline{x} = 100$$ and standard deviation $$s = 15$$, what is the z score for a value $$x = 130$$?

Accepted Answer

$$z = \frac{130 - 100}{15} = 2.00$$

Question 3

A platelet count of 75 (in 1000 cells/μL) is observed in a population with mean $$\overline{x} = 239.4$$ and standard deviation $$s = 64.2. $$What is the z score for this platelet count?

Accepted Answer

$$z = \frac{75 - 239.4}{64.2} = -2.56$$

Question 4

Which of the following z scores indicates a significantly high value?

Accepted Answer

$$z = 2.10$$

Question 5

If a data value has a z score of $$-2.5$$, how would you interpret this value?

Accepted Answer

The value is significantly low.

Question 6

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

Accepted Answer

The mean

Question 7

How is the interquartile range (IQR) calculated?

Accepted Answer

$$IQR = Q_3$ - Q_1$

Question 8

A data set has $$Q_1 = 7.9$, Q_2$ = 13.9$$, and $$Q_3 = 21.5$. What is the midquartile range?

Accepted Answer

$$\frac{Q_3$ + Q_1$}{2} = \frac{21.5 + 7.9}{2} = 14.7$$

Question 9

Which of the following statements about percentiles is TRUE?

Accepted Answer

Percentiles divide a data set into 100 groups with about 1% of the values in each group.

Question 10

If the 40th percentile ($$P_{40}) of a $$data set is 11.7 Mbps, what does this mean?

Accepted Answer

40% of the data values are less than or equal to 11.7 Mbps.

Question 11

Which value in a data set is the same as the median?

Accepted Answer

$$Q_2$$

Question 12

A boxplot is constructed using which of the following values?

Accepted Answer

Minimum, $$Q_1$$, median, $$Q_3$$, maximum

Question 13

Which of the following is a correct method for identifying outliers using the interquartile range (IQR)?

Accepted Answer

A value is an outlier if it is below $$Q_1 - 1.5$$ 	imes IQR$$ or above Q_3$ + 1.5 	imes IQR.$$

Question 14

A data set has $$Q_1 = 7.9$, Q_3$ = 21.5. $$What is the range of values that are NOT considered outliers?

Accepted Answer

$$[7.9 - 1.5 	imes (21.5 - 7.9),\ 21.5 + 1.5 	imes (21.5 - 7.9)]$$

Question 15

Which of the following best describes the skewness of a data set if the boxplot shows the median closer to $$Q_1$$ and a longer whisker on the right?

Accepted Answer

The data is skewed to the right (positively skewed).

Question 16

If a value is at the 75th percentile, which quartile does it correspond to?

Accepted Answer

$$Q_3$$

Question 17

A data set has 50 values. What is the locator $$L$$ for the 40th percentile ($$k = 40$$)?

Accepted Answer

$$L = \frac{40}{100} 	imes 50 = 20$$

Question 18

Which of the following is TRUE about the calculation of quartiles and percentiles?

Accepted Answer

There is not universal agreement on a single procedure for calculating quartiles and percentiles.

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

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