Q: The range of a data set is calculated as:

$$\text{Range} = X_{\text{max}} - X_{\text{min}}$$

Question 1

Which of the following best describes a frequency distribution?

Accepted Answer

A table that shows classes or intervals of data with a count of the number of entries in each class.

Question 2

Given a data set with a minimum value of 7 and a maximum value of 86, and you want to create 7 classes, what is the appropriate class width?

Accepted Answer

$$\frac{86-7}{7} = 11.3$$, so round up to 12

Question 3

Which type of graph is most appropriate for displaying the frequency distribution of a quantitative data set?

Accepted Answer

Frequency histogram

Question 4

A frequency polygon is different from a histogram because:

Accepted Answer

It uses line segments to connect class midpoints, emphasizing continuous change.

Question 5

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

Accepted Answer

Range

Question 6

A data set has the following values: 5, 7, 9, 10, 11, 13, 14, 15, 16, 17, 18, 18, 20, 21, 37. What is the median?

Accepted Answer

15

Question 7

Which of the following statements about the mean is TRUE?

Accepted Answer

The mean is greatly affected by outliers.

Question 8

If a distribution is skewed right (positively skewed), which of the following is the correct order of mean, median, and mode?

Accepted Answer

Mode \u003c Median \u003c Mean

Question 9

The range of a data set is calculated as:

Accepted Answer

$$	ext{Range} = X_{	ext{max}} - X_{	ext{min}}$$

Question 10

Which formula is used to calculate the sample standard deviation $$s$$ for a data set with $$n$$ entries and sample mean $$\bar{x}$$?

Accepted Answer

$$s = \sqrt{\frac{\sum (x - \bar{x})^2$}{n-1}}$$

Question 11

According to the Empirical Rule, approximately what percent of data in a bell-shaped distribution lies within two standard deviations of the mean?

Accepted Answer

95%

Question 12

Chebychev’s Theorem states that for any data set, at least what proportion of the data lies within $$k=2$$ standard deviations of the mean?

Accepted Answer

$$1 - \frac{1}{k^2$} = 1 - \frac{1}{4} = 0.75$$

Question 13

A student scored in the 95th percentile on a standardized test. This means:

Accepted Answer

The student scored better than 95% of the other students.

Question 14

Which of the following is NOT a feature of a box-and-whisker plot?

Accepted Answer

It displays the mean of the data set.

Question 15

The z-score for a value $$x in a $$data set with mean $$\mu$$ and standard deviation $$\sigma is $$given by:

Accepted Answer

$$z = \frac{x - \mu}{\sigma}$$

Question 16

Which type of graph is best for showing the relationship between two quantitative variables, such as petal length and petal width in Fisher’s Iris data set?

Accepted Answer

Scatter plot

Question 17

A time series chart is most useful for:

Accepted Answer

Displaying how a quantitative variable changes over time.

Question 18

Which of the following is a correct interpretation of a relative frequency histogram?

Accepted Answer

The vertical axis shows the proportion of data in each class.

Question 19

If a data set is symmetric and bell-shaped, which measure of central tendency is most appropriate to describe a typical value?

Accepted Answer

Mean

Question 20

A Pareto chart is used to:

Accepted Answer

Display frequencies of categories in decreasing order.

Describing Data with Tables and Graphs: Frequency Distributions, Graphical Displays, and Measures of Central Tendency

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