Q: A value in a data set is considered an outlier if it is:

Less than $$Q_1 - 1.5$$ \times IQR$$ or greater than Q_3$ + 1.5 \times IQR$$

Question 1

A data set of exam scores is found to be skewed right. Which of the following statements best describes the relationship between the mean and the median for this data set?

Accepted Answer

The mean is substantially larger than the median.

Question 2

Given the following travel times to work (in minutes): 23, 36, 23, 18, 5, 26, 43, what is the population mean? Use the formula $$\mu = \frac{\sum x_i}{N}.$$

Accepted Answer

$$\mu = 24.86$$ minutes

Question 3

Which measure of central tendency is most resistant to extreme values (outliers)?

Accepted Answer

Median

Question 4

A sample of three travel times to work is: 5, 26, 36. What is the sample standard deviation? Use $$s = \sqrt{\frac{\sum (x_i - \bar{x})^2$}{n-1}}.$$

Accepted Answer

$$s = 15.82$$ minutes

Question 5

A bell-shaped distribution has a mean of 100 and a standard deviation of 10. According to the Empirical Rule, approximately what percentage of data falls between 80 and 120?

Accepted Answer

95%

Question 6

If a data set has a mean of 50 and a standard deviation of 5, what is the z-score for a value of 60? Use $$z = \frac{x - \mu}{\sigma}.$$

Accepted Answer

$$z = 2$$

Question 7

A student scored at the 90th percentile on a standardized test. What does this mean?

Accepted Answer

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

Question 8

Given the data set: 5, 18, 23, 23, 26, 36, 43, what is the interquartile range (IQR)? Use $$IQR = Q_3$ - Q_1$.

Accepted Answer

$$IQR = 13$$

Question 9

Which of the following is NOT part of the five-number summary?

Accepted Answer

Mean

Question 10

A boxplot of a data set shows the median closer to the lower quartile ($$Q_1) $$and a longer whisker on the upper end. What can you infer about the shape of the distribution?

Accepted Answer

The distribution is skewed right.

Question 11

If the range of a data set is 40 and the smallest value is 10, what is the largest value?

Accepted Answer

50

Question 12

Which of the following statements about Chebyshev’s Inequality is correct?

Accepted Answer

It applies to any data set, regardless of shape.

Question 13

A data set has $$Q_1 = 20$, Q_3$ = 40$$, and $$IQR = 20. $$What is the lower fence for detecting outliers? Use $$	ext{Lower fence} = Q_1$ - 1.5 	imes IQR.$$

Accepted Answer

Lower fence = -10

Question 14

A frequency distribution for car prices has midpoints $$x_i$$ and frequencies $$f_i. $$What is the formula for the approximate mean of the data?

Accepted Answer

$$\bar{x} = \frac{\sum x_i f_i}{\sum f_i}$$

Question 15

Bob mixes 1 lb of raisins at $$1.25/lb$$, 2 lbs of chocolate peanuts at $$3.25/lb$$, and 1.5 lbs of cashews at $$5.40/lb. $$What is the weighted mean price per pound? Use $$\bar{x}_w = \frac{\sum w_i x_i}{\sum w_i}.$$

Accepted Answer

$$\3.60$

Question 16

Which measure of dispersion is most appropriate to report when the data are skewed?

Accepted Answer

Interquartile range

Question 17

A data set has a mean of 100 and a standard deviation of 20. According to Chebyshev’s Inequality, at least what percentage of data falls within 2 standard deviations of the mean?

Accepted Answer

75%

Question 18

Which of the following best describes the mode?

Accepted Answer

The value that occurs most frequently in a data set.

Question 19

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

Accepted Answer

Mean and standard deviation

Question 20

A value in a data set is considered an outlier if it is:

Accepted Answer

Less than $$Q_1 - 1.5$$ 	imes IQR$$ or greater than Q_3$ + 1.5 	imes IQR$$

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

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