Q: A data set has $$Q_1 = 735$, Q_3$ = 4668$$, and $$IQR = 3933. $$What is the upper fence for detecting outliers?

$$4668 + 1.5 \times 3933 = 10567.5$$

Q: A sample of exam scores has a mean of 79 and a standard deviation of 9.8. According to the Empirical Rule, what is the approximate range of scores that contains 95% of the data?

$$79 \pm 2 \times 9.8 = [59.4, 98.6]$$

Question 1

A pharmaceutical company collects the following data on the number of days patients experience side effects from a new drug: 2, 3, 3, 4, 5, 7, 8, 8, 8, 10. What is the mode of this data set?

Accepted Answer

8

Question 2

A researcher is analyzing the annual incomes (in thousands of dollars) of a group of people: 35, 38, 40, 42, 45, 47, 50, 52, 55, 200. Which measure of central tendency is most resistant to the outlier in this data set?

Accepted Answer

Median

Question 3

Given the following exam scores: 62, 68, 71, 74, 77, 82, 84, 88, 90, 94, what is the median score?

Accepted Answer

$$M = \frac{77 + 82}{2} = 79.5$$

Question 4

A population consists of the following values: 5, 7, 9, 10, 12. What is the population mean $$\mu$$?

Accepted Answer

$$\mu = \frac{5 + 7 + 9 + 10 + 12}{5} = 8.6$$

Question 5

Which of the following statements about the mean and median is TRUE for a distribution that is skewed right?

Accepted Answer

The mean is greater than the median.

Question 6

A sample of four students’ test scores are: 62, 88, 77, 68. What is the sample mean $$\bar{x}$$?

Accepted Answer

$$\bar{x} = \frac{62 + 88 + 77 + 68}{4} = 73.75$$

Question 7

The birth weights of 50 babies are approximately bell-shaped with a mean of 7.49 pounds and a standard deviation of 0.8 pounds. According to the Empirical Rule, about what percentage of babies have birth weights between 6.69 and 8.29 pounds?

Accepted Answer

Approximately 68%

Question 8

A student’s SAT Mathematics score is in the 74th percentile. What does this mean?

Accepted Answer

74% of students scored less than or equal to this score.

Question 9

Given a data set with $$Q_1 = 20$, Q_3$ = 50$$, and $$IQR = Q_3$ - Q_1$, what is the interquartile range?

Accepted Answer

$$IQR = 50 - 20 = 30$$

Question 10

A data set has $$Q_1 = 735$, Q_3$ = 4668$$, and $$IQR = 3933. $$What is the upper fence for detecting outliers?

Accepted Answer

$$4668 + 1.5 	imes 3933 = 10567.5$$

Question 11

Which of the following is the correct formula for the population standard deviation $$\sigma$$?

Accepted Answer

$$\sigma = \sqrt{\frac{\sum (x_i - \mu)^2$}{N}}$$

Question 12

A student’s test score is 88. The class mean is 79 and the standard deviation is 9.8. What is the student’s z-score?

Accepted Answer

$$z = \frac{88 - 79}{9.8} = 0.92$$

Question 13

Which of the following best describes the five-number summary?

Accepted Answer

Minimum, $$Q_1$$, Median, $$Q_3$$, Maximum

Question 14

A boxplot is constructed for a data set. If the median is closer to $$Q_1$$ than $$Q_3$$ and the right whisker is longer than the left, what is the likely shape of the distribution?

Accepted Answer

Skewed right

Question 15

A sample of exam scores has a mean of 79 and a standard deviation of 9.8. According to the Empirical Rule, what is the approximate range of scores that contains 95% of the data?

Accepted Answer

$$79 \pm 2 	imes 9.8 = [59.4, 98.6]$$

Question 16

Which measure of dispersion is most appropriate to report for a data set that is highly skewed?

Accepted Answer

Interquartile range

Question 17

A data set has the following values: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 3. What is the mode?

Accepted Answer

0

Question 18

If a distribution is symmetric, which measure of central tendency and dispersion should be reported?

Accepted Answer

Mean and standard deviation

Question 19

A sample has $$n = 4$$ values: 62, 88, 77, 68. The sample mean is $$\bar{x} = 73.75. $$What is the sample variance $$s^2$$?

Accepted Answer

$$s^2$$ = \frac{384.75}{3} = 128.25$$

Numerically Summarizing Data: Measures of Central Tendency, Dispersion, Position, and Boxplots

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