Question 1

Which of the following best describes the difference between the population mean and the sample mean?

Accepted Answer

The population mean is a parameter, while the sample mean is a statistic.

Question 2

Given the data set: 4, 1, 5, 3, 6, 1, 3, what is the sample mean?

Accepted Answer

$$\overline{x} = \dfrac{4 + 1 + 5 + 3 + 6 + 1 + 3}{7} = 3.29$$

Question 3

Which measure of central tendency is most resistant to outliers?

Accepted Answer

Median

Question 4

A data set has the following values: 2, 5, 7, 8, 100. Which measure of central tendency best describes the typical value?

Accepted Answer

Median, because the data set is skewed by an outlier.

Question 5

If a data set is perfectly symmetric and contains no outliers, which of the following is true?

Accepted Answer

Mean = Median = Mode

Question 6

Given the data set: 10, 12, 14, 16, 18, what is the median?

Accepted Answer

The median is $$14$$

Question 7

Which of the following formulas correctly represents the population mean $$\mu$$ for $$N$$ observations $$x_1$$, $$x_2$$, ..., x_N$$?

Accepted Answer

$$\mu = \dfrac{\sum_{i=1}^{N} x_i}{N}$$

Question 8

A hospital administrator wants to summarize the typical length of stay for patients. The data is highly skewed to the right due to a few patients with extremely long stays. Which measure should be used?

Accepted Answer

Median, because it is resistant to extreme values.

Question 9

Which of the following statements about the mode is correct?

Accepted Answer

A data set can have no mode, one mode, or more than one mode.

Question 10

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

Accepted Answer

There is no mode.

Question 11

A data set has the following values: 5, 7, 7, 8, 10, 10, 12. What is the mode?

Accepted Answer

The data set is bimodal: 7 and 10.

Question 12

Which of the following best describes a right-skewed distribution?

Accepted Answer

Mean $$\u003e$$ Median \u003e Mode

Question 13

A real estate agent is analyzing home prices in a city. Most homes are priced between $$200,000 and 400$$,000, but a few luxury homes are priced above $2,000,000. Which measure of central tendency should the agent use to describe a typical home price?

Accepted Answer

Median, because it is resistant to outliers.

Question 14

Which of the following is NOT a step in finding the median of a data set?

Accepted Answer

Add all the values and divide by the number of observations.

Question 15

Suppose a data set has a mean of 245 and a median of 140. What can you infer about the shape of the distribution?

Accepted Answer

The distribution is right-skewed.

Question 16

Which of the following is the correct formula for the sample mean $$\overline{x}$$ for $$n$$ observations $$x_1$$, $$x_2$$, ..., x_n$$?

Accepted Answer

$$\overline{x} = \dfrac{\sum_{i=1}^{n} x_i}{n}$$

Question 17

A data set has values: 3, 5, 7, 9, 11. What is the median?

Accepted Answer

The median is $$7$$

Question 18

Which of the following best describes a resistant numerical summary?

Accepted Answer

A summary that is not affected substantially by extreme values.

Question 19

If a data set is left-skewed, which of the following is most likely true?

Accepted Answer

Mean $$\u003c$$ Median $$\u003c$$ Mode

Question 20

A teacher records the following test scores: 70, 75, 80, 85, 90, 95, 100. If a student scores 300 on a retake, which measure of central tendency will be most affected?

Accepted Answer

Mean

Measures of Central Tendency: Mean, Median, and Mode

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