Question 1

Given the data set: 3, 4, 4, 4, 5, 6, 7, 8, 11, what is the mean of the distribution? Use the formula $$\mu = \frac{\sum_{i=1}^n x_i}{n}.$$

Accepted Answer

$$\mu = 5.78$$

Question 2

For the same data set (3, 4, 4, 4, 5, 6, 7, 8, 11), what is the median? Recall that for an odd number of values, the median is the middle value when ordered.

Accepted Answer

The median is 5

Question 3

What is the mode of the data set: 3, 4, 4, 4, 5, 6, 7, 8, 11?

Accepted Answer

The mode is 4

Question 4

If you calculate the sum of all the positive distances from the mean and the sum of all the negative distances from the mean for any data set, what will their total sum always be?

Accepted Answer

Zero

Question 5

A dotplot is created for the data set 3, 4, 4, 4, 5, 6, 7, 8, 11. Which value would be closest to the mean on the dotplot?

Accepted Answer

5.78

Question 6

In a highly skewed distribution of salaries for professional baseball players, which measure of center is likely to be a better representative of a typical player's salary?

Accepted Answer

Median

Question 7

What is the main advantage of the median compared to the mean in a skewed distribution?

Accepted Answer

The median is less affected by extreme values (outliers)

Question 8

What is the main advantage of the mean compared to the median?

Accepted Answer

The mean uses all data values in its calculation

Question 9

Given the frequency distribution: Value: 3, 4, 5, 6, 7, 8, 11; Frequency: 1, 3, 1, 1, 1, 1, 1. What is the total number of data points?

Accepted Answer

9

Question 10

If the mean salary of baseball players is much higher than the median, what does this indicate about the distribution of salaries?

Accepted Answer

The distribution is right-skewed (positively skewed)

Question 11

Suppose you add a new value, 20, to the data set 3, 4, 4, 4, 5, 6, 7, 8, 11. Which measure of center will be most affected?

Accepted Answer

Mean

Question 12

Which of the following is NOT a measure of center?

Accepted Answer

Range

Question 13

If a data set has two modes, what is it called?

Accepted Answer

Bimodal

Question 14

Given the formula for the mean $$\mu = \frac{\sum_{i=1}^n x_i}{n}$$, what does $$n$$ represent?

Accepted Answer

The number of data points

Question 15

If the sum of all distances from the mean is always zero, what does this property help us understand about the mean?

Accepted Answer

The mean is the balance point of the data

Question 16

A data set has the following values: 3, 4, 4, 4, 5, 6, 7, 8, 11. What is the position of the median in the ordered list?

Accepted Answer

5th value

Question 17

Which of the following statements is true regarding the mean and median in a symmetric distribution?

Accepted Answer

The mean and median are equal

Question 18

If a data set is summarized in a frequency table, which formula should you use to calculate the mean?

Accepted Answer

$$\mu = \frac{\sum_{i=1}^k x_i f_i}{N}$$

Question 19

A histogram of baseball player salaries is highly right-skewed. Which measure of center is most likely to be pulled in the direction of the skew?

Accepted Answer

Mean

Question 20

Which of the following best describes why the mean is not always the best measure of center for a data set with outliers?

Accepted Answer

The mean is sensitive to extreme values

Measures of Center and Data Representation in Statistics

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