Question 1

Which of the following best describes the sample mean $$\bar{x}$$ for a set of $$n$$ measurements $$x_1$$, $$x_2$$, ..., x_n$$?

Accepted Answer

$$\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}$$

Question 2

A sociologist is studying household incomes in a city where a few households have extremely high incomes. Which measure of central tendency would best represent the 'typical' household income?

Accepted Answer

The median

Question 3

Given the following sample data: 5, 3, 8, 5, 6. What is the sample mean $$\bar{x}$$?

Accepted Answer

$$\bar{x} = 5.4$$

Question 4

Which symbol is used to denote the population mean?

Accepted Answer

$$\mu$$

Question 5

If a data set is rightward skewed, which of the following relationships between the mean and median is most likely?

Accepted Answer

Mean $$\u003e$$ Median

Question 6

A set of exam scores is: 70, 75, 80, 85, 90, 95, 100. What is the median score?

Accepted Answer

85

Question 7

Which of the following statements is TRUE regarding the sensitivity of the mean and median to outliers?

Accepted Answer

The mean is more sensitive to outliers than the median.

Question 8

A data set has the following values: 2, 4, 4, 4, 5, 7, 9. What is the mode?

Accepted Answer

4

Question 9

If a data set is symmetric, what can you say about the mean and the median?

Accepted Answer

The mean equals the median.

Question 10

A researcher collects EPA mileage ratings for 100 cars and calculates a sample mean $$\bar{x} = 36.9940. $$What is the best interpretation of this value?

Accepted Answer

It is an estimate of the population mean $$\mu$$ for all cars.

Question 11

Given the sample: 5, 7, 4, 5, 20, 6, 2, what is the median?

Accepted Answer

5

Question 12

Which of the following is NOT a measure of central tendency?

Accepted Answer

Range

Question 13

A data set is leftward skewed. Which of the following is most likely true?

Accepted Answer

Mean $$\u003c$$ Median

Question 14

Which of the following best describes the mode?

Accepted Answer

The value that occurs most frequently in the data set.

Question 15

A sample of 10 taste testers rated a sauce: 8, 7, 9, 6, 8, 10, 9, 9, 5, 7. What is the mode?

Accepted Answer

9

Question 16

Which of the following formulas correctly represents the calculation of the sample mean for $$n$$ measurements?

Accepted Answer

$$\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}$$

Question 17

Which symbol is used to denote the sample median?

Accepted Answer

$$M$$

Question 18

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

Accepted Answer

6

Question 19

Which of the following is a reason to use the median instead of the mean as a measure of central tendency?

Accepted Answer

The data set contains extreme values (outliers).

Question 20

If the mean and median of a data set are equal, what does this suggest about the distribution?

Accepted Answer

The distribution is symmetric.

Numerical Measures of Central Tendency in Statistics

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