Q: A data set has $$Q_1 = 20$, Q_3$ = 40$$, and $$IQR = 20. $$What is the upper fence for detecting outliers?

$$Q_3 + 1.5$$ \times IQR = 40 + 1.5 \times 20 = 70$$

Question 1

A data set of exam scores is approximately bell-shaped with a mean of 80 and a standard deviation of 5. According to the Empirical Rule, what percentage of students scored between 75 and 85?

Accepted Answer

Approximately 68%

Question 2

Given a bell-shaped distribution with mean $$\mu = 100$$ and standard deviation $$\sigma = 20$$, what is the range of values that contains approximately 99.7% of the data?

Accepted Answer

$$40 to$$ $$160$$

Question 3

A student scored 92 on a test where the class mean was 85 and the standard deviation was 3. What is the student's z-score?

Accepted Answer

$$z = \frac{92 - 85}{3} = 2.33$$

Question 4

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

Accepted Answer

The difference between the third and first quartiles: $$IQR = Q_3$ - Q_1$

Question 5

A data set has $$Q_1 = 20$, Q_3$ = 40$$, and $$IQR = 20. $$What is the upper fence for detecting outliers?

Accepted Answer

$$Q_3 + 1.5$$ 	imes IQR = 40 + 1.5 	imes 20 = 70$$

Question 6

Which of the following statements about the five-number summary is TRUE?

Accepted Answer

It includes the minimum, $$Q_1$$, median, $$Q_3$$, and maximum.

Question 7

If a value in a data set is below the lower fence, what does this indicate?

Accepted Answer

The value is considered an outlier.

Question 8

A boxplot of a data set shows the median line closer to the left edge of the box and the right whisker is longer than the left. What does this indicate about the distribution?

Accepted Answer

The distribution is skewed right.

Question 9

Which of the following is NOT a possible cause of an outlier in a data set?

Accepted Answer

A value that is the median of the data

Question 10

A student’s test score is at the 90th percentile. What does this mean?

Accepted Answer

The student scored higher than 90% of the students.

Question 11

Given the data set: 2, 4, 7, 10, 12, 15, 18, 20, 25, what is the median?

Accepted Answer

12

Question 12

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

Accepted Answer

The value is 2.5 standard deviations below the mean.

Question 13

Which of the following is a resistant measure of dispersion?

Accepted Answer

Interquartile range (IQR)

Question 14

A data set has a minimum of 5, $$Q_1 = 10$, median = 15, Q_3$ = 20$$, and maximum = 30. What is the five-number summary?

Accepted Answer

5, 10, 15, 20, 30

Question 15

If a distribution is symmetric, how will the boxplot appear?

Accepted Answer

The median line is in the center of the box and the whiskers are approximately equal in length.

Question 16

A researcher finds that a data value is above the upper fence. What should the researcher do?

Accepted Answer

Investigate the value as a potential outlier.

Question 17

Which of the following best describes a percentile?

Accepted Answer

A value below which a given percentage of observations fall.

Question 18

If a data set has $$Q_1 = 15$, Q_3$ = 35$$, and a value of 60, is 60 an outlier?

Accepted Answer

No, because it is less than $$Q_3 + 1.5$$ 	imes IQR = 35 + 1.5 	imes (35-15) = 65$$

Question 19

Which of the following is NOT included in the five-number summary?

Accepted Answer

The mean

Question 20

A data set is highly skewed to the left. Which of the following is most likely true about its boxplot?

Accepted Answer

The left whisker is longer and the median is to the right of center in the box.

Statistical Analysis Chapter 3: Measures of Position, The Five Number Summary, and Boxplots

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