Q: A company has 20 employees: 18 earn $$10,000, one earns 75$$,000, and one earns $200,000. What is the mean salary?

$$\dfrac{18 \times 10,000 + 75,000 + 200,000}{20} = 22,750$$

Question 1

Which of the following is the correct formula for the population mean $$\mu$$ given $$n$$ data values $$x_1$$, $$x_2$$, ..., x_n$$?

Accepted Answer

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

Question 2

A sample of roundtrip flight prices (in dollars) is: 872, 432, 397, 482, 782, 397. What is the mode of this data set?

Accepted Answer

$$397$$

Question 3

Which measure of central tendency is most appropriate to describe the typical salary in a company where most employees earn $$10,000, but the president earns 200$$,000 and the vice president earns $75,000?

Accepted Answer

Median

Question 4

Given the data set: 35, 40, 43, 40, 92, 39, 98, 39, 81, what is the median?

Accepted Answer

$$43$$

Question 5

If a distribution is symmetric (bell-shaped), which of the following statements is true?

Accepted Answer

The mean, median, and mode are all equal.

Question 6

A biologist records the number of times a certain phenotype appears in 10 samples: 2, 3, 3, 4, 4, 4, 5, 5, 6, 7. Which measure of central tendency best represents the most common phenotype?

Accepted Answer

Mode

Question 7

Which of the following statements about the mean is FALSE?

Accepted Answer

The mean is always one of the original data values.

Question 8

A data set has values: 10, 12, 14, 16, 18, 100. Which measure of central tendency is LEAST affected by the outlier 100?

Accepted Answer

Median

Question 9

In a negatively skewed (skewed left) distribution, which of the following is true?

Accepted Answer

The mean is less than the median.

Question 10

A uniform distribution is characterized by which property?

Accepted Answer

All entries or classes have equal or approximately equal frequencies.

Question 11

Given the data set: 1210, 546, 669, 612, 631, 682. Calculate the mean.

Accepted Answer

$$\dfrac{1210 + 546 + 669 + 612 + 631 + 682}{6} = 707.33$$

Question 12

Which of the following is NOT a property of the mode?

Accepted Answer

The mode is always unique for any data set.

Question 13

A set of test scores is: 43, 56, 61, 69, 74, 81, 92. What is the median?

Accepted Answer

$$69$$

Question 14

Which measure of central tendency is most appropriate for describing the center of a distribution of household trash weights that is positively skewed due to a few outliers?

Accepted Answer

Median

Question 15

If a data set has no repeated values, what is the mode?

Accepted Answer

There is no mode

Question 16

A company has 20 employees: 18 earn $$10,000, one earns 75$$,000, and one earns $200,000. What is the mean salary?

Accepted Answer

$$\dfrac{18 	imes 10,000 + 75,000 + 200,000}{20} = 22,750$$

Question 17

Which measure of central tendency is most appropriate for categorical data such as favorite colors or political affiliation?

Accepted Answer

Mode

Question 18

If a distribution is positively skewed, which statement is true?

Accepted Answer

The mean is greater than the median.

Question 19

A sample of flight prices (in dollars) is: 872, 432, 397, 482, 782, 397, 827. What is the mean price?

Accepted Answer

$$\dfrac{872 + 432 + 397 + 482 + 782 + 397 + 827}{7} = 527.86$$

2.3- Measures of Central Tendency and the Shape of Distributions

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