Question 1

Which of the following best describes the difference between a parameter and a statistic?

Accepted Answer

A parameter is a numerical summary of a population, while a statistic is a numerical summary of a sample.

Question 2

Given the data set: 23, 36, 23, 18, 5, 26, 43, what is the population mean ($$\mu$$)?

Accepted Answer

$$\mu = \frac{174}{7} = 24.9$$

Question 3

Which measure of central tendency is most appropriate to use when a data set contains extreme outliers?

Accepted Answer

Median

Question 4

A sample of three employees is selected from the population: 23, 36, 23, 18, 5, 26, 43. If the sample is 5, 36, 26, what is the sample mean ($$\overline{x}$$)?

Accepted Answer

$$\overline{x} = \frac{5 + 36 + 26}{3} = 22.3$$

Question 5

Which of the following statements about the median is correct?

Accepted Answer

The median is the value that lies in the middle of the data when arranged in ascending order.

Question 6

If a data set is skewed right, which of the following is true about the mean and median?

Accepted Answer

Mean is substantially larger than the median.

Question 7

Given the following wait times (in minutes) at two restaurants: Wendy’s (standard deviation = 0.738) and McDonald’s (standard deviation = 1.265), what can you conclude?

Accepted Answer

Wait times at McDonald’s are more dispersed than at Wendy’s.

Question 8

Which formula correctly represents the population standard deviation ($$\sigma$$)?

Accepted Answer

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

Question 9

A data set has $$Q_1 = 28$, Q_3$ = 38. $$What is the interquartile range (IQR)?

Accepted Answer

$$IQR = Q_3$ - Q_1$ = 10$$

Question 10

Which of the following best describes Chebyshev’s Inequality?

Accepted Answer

It states that at least $$\left(1 - \frac{1}{k^2$}\right)100\% of $$the data lie within $$k$$ standard deviations of the mean for any $$k \u003e 1.$$

Question 11

A student scores in the 70th percentile on the GRE. What does this mean?

Accepted Answer

The student scored higher than 70% of test-takers.

Question 12

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

Accepted Answer

Mean

Question 13

Given a data set with $$Q_1 = 12$, Q_3$ = 14.4$$, what is the lower fence for outlier detection?

Accepted Answer

$$Lower\ Fence = Q_1$ - 1.5(IQR) = 12 - 1.5(2.4) = 8.4$$

Question 14

If a value in a data set is greater than the upper fence, what does this indicate?

Accepted Answer

The value is an outlier.

Question 15

Which of the following is the correct formula for a z-score for a population?

Accepted Answer

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

Question 16

A data set has a mean of 50 and a standard deviation of 5. What is the z-score for a value of 65?

Accepted Answer

$$z = \frac{65 - 50}{5} = 3$$

Question 17

Which measure of dispersion is most appropriate to report for a skewed distribution?

Accepted Answer

Interquartile range

Question 18

If a data set has no repeated values, what can be said about its mode?

Accepted Answer

The data set has no mode.

Question 19

Which of the following best describes the Empirical Rule for a bell-shaped distribution?

Accepted Answer

Approximately 68% of data lie within 1 standard deviation, 95% within 2, and 99.7% within 3 standard deviations of the mean.

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

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