Q: Which formula correctly calculates the mean of a population with $$N$$ observations $$x_1$$, $$x_2$$, ..., x_N$$?

$$\text{Mean} = \frac{x_1$ + x_2$ + \cdots + x_N}{N}$$

Question 1

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

Accepted Answer

The population mean is a parameter describing the entire population, while the sample mean is a statistic describing a subset of the population.

Question 2

Given the data set: 5, 10, 15, 20, 25, 30, 35, what is the mean of the data?

Accepted Answer

$$\frac{5+10+15+20+25+30+35}{7} = 20$$

Question 3

A data set contains the following values: 2, 4, 4, 5, 7, 8, 9. What is the median?

Accepted Answer

$$5$$

Question 4

Which measure of central tendency is most resistant to outliers?

Accepted Answer

Median

Question 5

A start-up company has employee commute times (in minutes): 23, 36, 23, 18, 5, 26, 43. If a new employee with a 130-minute commute is added, which measure of central tendency will be most affected?

Accepted Answer

Mean

Question 6

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

Accepted Answer

Mean is substantially larger than the median.

Question 7

Given the data set: 1, 2, 2, 3, 4, 4, 5, what is the mode?

Accepted Answer

$$2$$ and $$4 ($$bimodal)

Question 8

Which formula correctly calculates the mean of a population with $$N$$ observations $$x_1$$, $$x_2$$, ..., x_N$$?

Accepted Answer

$$	ext{Mean} = \frac{x_1$ + x_2$ + \cdots + x_N}{N}$$

Question 9

A sample of 7 travel times (in minutes) is: 5, 18, 23, 23, 26, 36, 43. What is the median?

Accepted Answer

$$23$$

Question 10

Which of the following scenarios would most likely result in the mean and median being close in value?

Accepted Answer

A symmetric, bell-shaped distribution

Question 11

A data set contains the following values: 1, 2, 2, 3, 4, 5, 6. What is the mean?

Accepted Answer

$$\frac{1+2+2+3+4+5+6}{7} = 3.29$$

Question 12

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

Accepted Answer

There is no mode.

Question 13

Which measure of central tendency is most appropriate for qualitative data?

Accepted Answer

Mode

Question 14

A data set is: 1, 2, 3, 4, 5, 6, 7, 8. What is the median?

Accepted Answer

$$\frac{4+5}{2} = 4.5$$

Question 15

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

Accepted Answer

Range

Question 16

In a data set with values: 1, 2, 2, 3, 4, 5, 6, which value divides the data into two equal halves?

Accepted Answer

Median

Question 17

If the mean net worth of households is $$301,000$$ and the median is $$45,000$$, which measure better describes the typical household net worth?

Accepted Answer

Median

Question 18

Which of the following is true about the mean in a skewed distribution?

Accepted Answer

The mean is pulled in the direction of the skew.

Question 19

A data set has values: 1, 2, 3, 4, 5, 100. Which measure of central tendency is least affected by the value 100?

Accepted Answer

Median

Question 20

Which of the following best describes the mode?

Accepted Answer

The value that occurs most frequently in a data set.

Ch. 3- Measures of Central Tendency: Mean, Median, and Mode

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