Q: Given a data set with $$n = 20$$ entries, and a value $$x$$ with 15 entries less than $$x$$, what is the percentile rank of $$x$$?

$$Percentile = \frac{15}{20} \times 100 = 75$$

Q: A data set has $$Q_1 = 25$, Q_3$ = 45$$, and $$IQR = 20. $$Which value would be considered an outlier?

A value greater than $$Q_3 + 1.5$$ \times IQR = 45 + 30 = 75$$

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: 10, 12, 14, 16, 18, 20, 22, what is the median?

Accepted Answer

$$16$$

Question 4

If a data entry is less than $$Q_1 - 1.5$$ 	imes IQR$$, what can you conclude about this entry?

Accepted Answer

It is an outlier.

Question 5

A student scored 85 on a test where the mean was 75 and the standard deviation was 5. What is the student's z-score?

Accepted Answer

$$z = \frac{85 - 75}{5} = 2$$

Question 6

Which of the following statements about quartiles is correct?

Accepted Answer

The first quartile ($$Q_1) is $$the value below which about 25% of the data fall.

Question 7

A data set has $$Q_1 = 20$, Q_3$ = 40$$, and a minimum value of 10. What is the interquartile range?

Accepted Answer

$$IQR = 40 - 20 = 20$$

Question 8

If a student’s SAT score is at the 90th percentile, what does this mean?

Accepted Answer

The student scored higher than 90% of the other students.

Question 9

Given a data set with $$n = 20$$ entries, and a value $$x$$ with 15 entries less than $$x$$, what is the percentile rank of $$x$$?

Accepted Answer

$$Percentile = \frac{15}{20} 	imes 100 = 75$$

Question 10

A box-and-whisker plot for a data set shows a long left whisker and a short right whisker. What does this suggest about the data?

Accepted Answer

There may be a possible outlier on the left side.

Question 11

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

Accepted Answer

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

Question 12

A data set has $$Q_1 = 25$, Q_3$ = 45$$, and $$IQR = 20. $$Which value would be considered an outlier?

Accepted Answer

A value greater than $$Q_3 + 1.5$$ 	imes IQR = 45 + 30 = 75$$

Question 13

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

Accepted Answer

The mean

Question 14

If a value in a data set has a z-score of $$-2.5$$, what does this indicate?

Accepted Answer

The value is 2.5 standard deviations below the mean.

Question 15

A researcher collects the following data set: 5, 7, 8, 12, 15, 18, 20. What is the third quartile ($$Q_3$$)?

Accepted Answer

$$18$$

Question 16

Which of the following best describes a percentile?

Accepted Answer

A value that divides the data set into 100 equal parts.

Question 17

A hospital administrator wants to know if a patient’s blood pressure is unusually high compared to the hospital’s average. The mean systolic blood pressure is 120 mmHg with a standard deviation of 10 mmHg. The patient’s blood pressure is 145 mmHg. What is the z-score?

Accepted Answer

$$z = \frac{145 - 120}{10} = 2.5$$

Question 18

Which of the following is a correct interpretation of the interquartile range (IQR)?

Accepted Answer

It measures the spread of the middle 50% of the data.

Question 19

A data set has a minimum value of 12, $$Q_1 = 18$, median = 25, Q_3$ = 32$$, and maximum value of 40. Which value is the median?

Accepted Answer

$$25$$

Descriptive Statistics: Measures of Position

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