Q: Which formula is used to calculate the percentile rank of a specific data entry $$x in a $$data set?

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

Q: Which of the following statements about outliers is correct when using the interquartile range (IQR)?

Any data entry less than $$Q_1 - 1.5$$ \times IQR$$ or greater than Q_3$ + 1.5 \times IQR is $$considered an outlier.

Q: If a data set has $$Q_1 = 25$, Q_3$ = 35$$, and an outlier is defined as any value less than $$Q_1 - 1.5$$ \times IQR$$, what is the cutoff value for a low outlier?

$$25 - 1.5 \times (35 - 25) = 10$$

Question 1

Which of the following best describes the interquartile range (IQR) of a data set?

Accepted Answer

The difference between the third quartile ($$Q_3) $$and the first quartile ($$Q_1$$): $$IQR = Q_3$ - Q_1$

Question 2

A box-and-whisker plot is constructed using which of the following components?

Accepted Answer

Minimum, first quartile, median, third quartile, and maximum

Question 3

Given the data set: 19, 30, 39, 44, 45, 46, 48, 48, 48, 48, 55, 55, 55, 55, 56, 57, 57, 58, 58, 59, 59, 59, 60, 61, 61. What is the percentile rank of the value 57?

Accepted Answer

60th percentile

Question 4

If the first quartile ($$Q_1) of a $$data set is 47 and the third quartile ($$Q_3) is 58.5$$, what is the interquartile range (IQR)?

Accepted Answer

$$IQR = 58.5 - 47 = 11.5$$

Question 5

A student scored 1350 on the SAT, which is at the 90th percentile. What does this mean?

Accepted Answer

The student scored higher than 90% of the test-takers.

Question 6

Which formula is used to calculate the percentile rank of a specific data entry $$x in a $$data set?

Accepted Answer

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

Question 7

The mean speed of vehicles on a highway is 56 mph with a standard deviation of 4 mph. What is the z-score for a car traveling at 62 mph?

Accepted Answer

$$z = \frac{62 - 56}{4} = 1.5$$

Question 8

Which of the following statements about outliers is correct when using the interquartile range (IQR)?

Accepted Answer

Any data entry less than $$Q_1 - 1.5$$ 	imes IQR$$ or greater than Q_3$ + 1.5 	imes IQR is $$considered an outlier.

Question 9

A 6-foot-tall woman has a mean height of 64.3 inches and a standard deviation of 2.8 inches in her population. What is her z-score?

Accepted Answer

$$z = \frac{72 - 64.3}{2.8} \approx 2.75$$

Question 10

Which of the following best describes the second quartile ($$Q_2) of a $$data set?

Accepted Answer

It is the value below which about 50% of the data fall (the median).

Question 11

A box-and-whisker plot for college tuition shows a left whisker much longer than the right. What does this suggest about the data?

Accepted Answer

There is a possible outlier on the lower end of the data.

Question 12

Which of the following is NOT part of the five-number summary required for a box-and-whisker plot?

Accepted Answer

The mean

Question 13

If a data set has $$Q_1 = 25$, Q_3$ = 35$$, and an outlier is defined as any value less than $$Q_1 - 1.5$$ 	imes IQR$$, what is the cutoff value for a low outlier?

Accepted Answer

$$25 - 1.5 	imes (35 - 25) = 10$$

Question 14

Which of the following best describes a z-score?

Accepted Answer

The number of standard deviations a value is from the mean.

Question 15

A data set has a minimum value of 24, $$Q_1 = 26$, median = 31, Q_3$ = 35$$, and maximum value of 39. Which value represents the third quartile?

Accepted Answer

35

Question 16

If a value in a data set has a z-score of $$-2.25$$, what does this indicate?

Accepted Answer

The value is 2.25 standard deviations below the mean.

Question 17

Which of the following is a correct interpretation of the 75th percentile in a data set?

Accepted Answer

75% of the data values are less than or equal to this value.

Descriptive Statistics: Measures of Position and Standard Scores

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