Q: Which formula is used to find the percentile that corresponds to a specific data entry in an ordered data set?

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

Q: Which formula is used to calculate the standard score (z-score) for a data value $$x$$?

$$z = \frac{x - \text{mean}}{\text{standard deviation}}$$

Question 1

Which of the following best describes the first quartile ($$Q_1) in a $$data set?

Accepted Answer

It is the value below which 25% of the data fall.

Question 2

Given the following ordered data set: 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, what is the third quartile ($$Q_3$$)?

Accepted Answer

33

Question 3

Which formula correctly calculates the interquartile range (IQR)?

Accepted Answer

$$\mathrm{IQR} = Q_3$ - Q_1$

Question 4

A data set has $$Q_1 = 20$ and Q_3$ = 40. $$Which of the following values would be considered an outlier according to the 1.5*IQR rule?

Accepted Answer

10

Question 5

Which of the following is NOT a required value for constructing a box-and-whisker plot?

Accepted Answer

Mean

Question 6

A box-and-whisker plot is most useful for:

Accepted Answer

Highlighting the spread and identifying outliers in a data set

Question 7

If a data set has a minimum value of 10, $$Q_1 = 20$, median = 30, Q_3$ = 40$$, and maximum value of 50, which interval contains the middle 50% of the data?

Accepted Answer

20 to 40

Question 8

Which formula is used to find the percentile that corresponds to a specific data entry in an ordered data set?

Accepted Answer

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

Question 9

A student scored 84 on a test. If 32 out of 40 students scored less than 84, what is the percentile rank of the student?

Accepted Answer

82nd percentile

Question 10

Which formula is used to calculate the standard score (z-score) for a data value $$x$$?

Accepted Answer

$$z = \frac{x - 	ext{mean}}{	ext{standard deviation}}$$

Question 11

A highway has a mean speed of 65 mph and a standard deviation of 5 mph. What is the z-score for a car traveling at 75 mph?

Accepted Answer

$$z = 2$$

Question 12

If a student’s z-score is -1.5, what does this indicate about their score relative to the mean?

Accepted Answer

The score is 1.5 standard deviations below the mean.

Question 13

A 6-foot-tall man has a mean height of 69.9 inches and a standard deviation of 2.8 inches. What is his z-score?

Accepted Answer

$$z = 3.0$$

Question 14

Why is it useful to compare z-scores from different data sets?

Accepted Answer

Because z-scores allow comparison of relative positions regardless of units or scales.

Question 15

Which of the following statements about percentiles is TRUE?

Accepted Answer

The 25th percentile is equivalent to the first quartile ($$Q_1).$$

Question 16

A data set has $$Q_1 = 15$, Q_3$ = 35$$, and IQR = 20. Which value would be considered an outlier?

Accepted Answer

5

Question 17

Which step is NOT part of drawing a box-and-whisker plot?

Accepted Answer

Plotting the mean as a central point

Question 18

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 19

If a value is greater than $$Q_3 + 1.5$$ 	imes \mathrm{IQR}$$, what does this indicate?

Accepted Answer

The value is a potential outlier.

Measures of Position in Statistics: Quartiles, Interquartile Range, Percentiles, and Standard Scores

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