$\text{range} = \text{max} - \text{min}$

$\text{relative frequency} = \frac{f}{n}$

A data value above $Q_3 + 1.5 \times IQR$ or below $Q_1 - 1.5 \times IQR$

Question 1

Which of the following best describes the difference between a population and a sample in statistics?

Accepted Answer

A population includes all possible data values, while a sample is a subset of those values.

Question 2

Given a frequency distribution with class lower limits of 10, 20, 30, and 40, what is the class width $w$?

Accepted Answer

$w = 10$

Question 3

If a dataset has a mean of 50 and a standard deviation of 5, what is the z-score for a data value of 60?

Accepted Answer

$z = \frac{60 - 50}{5} = 2$

Question 4

Which of the following is the formula for the range of a dataset?

Accepted Answer

$	ext{range} = 	ext{max} - 	ext{min}$

Question 5

A histogram of exam scores is bell-shaped and symmetric. Which statement is most likely true?

Accepted Answer

The mean and median are approximately equal.

Question 6

Which formula is used to calculate the relative frequency of a class in a frequency distribution?

Accepted Answer

$	ext{relative frequency} = \frac{f}{n}$

Question 7

If the lower class limits in a frequency distribution are 5, 15, 25, and 35, what is the class width $w$?

Accepted Answer

$w = 10$

Question 8

Which of the following is the formula for the z-score of a data value $x$?

Accepted Answer

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

Question 9

According to the Empirical Rule, approximately what percentage of data values are within 2 standard deviations of the mean in a normal distribution?

Accepted Answer

95%

Question 10

Which of the following describes an outlier using the interquartile range (IQR)?

Accepted Answer

A data value above $Q_3 + 1.5 	imes IQR$ or below $Q_1 - 1.5 	imes IQR$

Question 11

A dataset has $Q_1 = 20$, $Q_3 = 40$. What is the interquartile range (IQR)?

Accepted Answer

$IQR = 40 - 20 = 20$

Question 12

Which of the following is NOT part of the 5-number summary?

Accepted Answer

Mean

Question 13

A right-skewed histogram of household incomes is observed. Which statement is most likely true?

Accepted Answer

The mean is greater than the median.

Question 14

If a sample has data values: 2, 4, 6, 8, what is the sample mean $\bar{x}$?

Accepted Answer

$\bar{x} = \frac{2 + 4 + 6 + 8}{4} = 5$

Question 15

Which of the following is a parameter, not a statistic?

Accepted Answer

Population mean $\mu$

Question 16

A dataset has a minimum value of 5 and a maximum value of 25. What is the range?

Accepted Answer

$25 - 5 = 20$

Question 17

Which of the following best describes the median?

Accepted Answer

The value that divides the dataset into two equal halves.

Question 18

If 68% of data values are within 1 standard deviation of the mean, what percentage are within 3 standard deviations according to the Empirical Rule?

Accepted Answer

99.7%

Question 19

Which of the following is the formula for sample variance $s^2$?

Accepted Answer

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

Fundamentals of Descriptive Statistics: Populations, Frequency Distributions, and Data Variation

Study Guide - Practice Questions