$$R = \text{largest data value} - \text{smallest data value}$$

Question 1

Which of the following best describes the arithmetic mean of a variable from raw data?

Accepted Answer

It is computed by adding all the values of the variable and dividing by the number of values.

Question 2

Given the population data set: 23, 24, 21, 18, 15, 24, 43, what is the population mean $$\mu$$?

Accepted Answer

$$\mu = \frac{23 + 24 + 21 + 18 + 15 + 24 + 43}{7} = 24$$

Question 3

Which formula is used to calculate the sample mean $$\bar{x}$$?

Accepted Answer

$$\bar{x} = \frac{\sum x_i}{n}$$

Question 4

What does it mean for a statistic to be resistant?

Accepted Answer

It is not affected by extreme observations (very large or small values).

Question 5

How do you find the median of a data set with an odd number of observations?

Accepted Answer

Arrange the data in ascending order and select the middle value.

Question 6

Given the data set: 23, 24, 21, 18, 15, 24, 43, what is the median?

Accepted Answer

23

Question 7

Which of the following is the correct formula for the range $$R of a $$variable?

Accepted Answer

$$R = 	ext{largest data value} - 	ext{smallest data value}$$

Question 8

What is the population standard deviation $$\sigma$$ formula?

Accepted Answer

$$\sigma = \sqrt{\frac{\sum (x_i - \mu)^2$}{N}}$$

Question 9

If a data set is bell-shaped, approximately what percentage of data falls within two standard deviations of the mean according to the Empirical Rule?

Accepted Answer

95%

Question 10

Given a sample mean $$\bar{x} = 36.8$$, sample standard deviation $$s = 2.9$$, and an observation $$x = 41.1$$, what is the sample z-score?

Accepted Answer

$$z = \frac{41.1 - 36.8}{2.9} = 1.48$$

Question 11

Which measure of central tendency is most appropriate for data that are skewed left or right?

Accepted Answer

Median

Question 12

How is the interquartile range (IQR) calculated?

Accepted Answer

$$IQR = Q_3$ - Q_1$

Question 13

Which of the following is NOT a step in constructing a boxplot?

Accepted Answer

Calculate the mean and standard deviation.

Question 14

If a data set has a symmetric distribution, what is the relationship between the mean and the median?

Accepted Answer

The mean is equal to the median.

Question 15

Which formula is used to check for outliers using quartiles?

Accepted Answer

Lower fence: $$Q_1 - 1.5$$ 	imes IQR$$, Upper fence: Q_3$ + 1.5 	imes IQR$$

Question 16

Which of the following best describes the mode of a variable?

Accepted Answer

The value that occurs most frequently in the data set.

Question 17

If the standard deviation of waiting times at Wendy's is larger than at McDonald's, what does this indicate?

Accepted Answer

Waiting times at Wendy's are more spread out than at McDonald's.

Question 18

Which of the following is NOT part of the five-number summary?

Accepted Answer

Mean

Question 19

What does the Empirical Rule state about data within three standard deviations of the mean in a bell-shaped distribution?

Accepted Answer

Approximately 99.7% of the data fall within three standard deviations of the mean.

Numerically Summarizing Data: Measures of Central Tendency, Dispersion, Position, and Visualization

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