Q: Which of the following is the correct formula for class width?

$$\text{Class width} = \text{Difference between two consecutive lower class limits}$$

Question 1

Which of the following best describes a frequency distribution?

Accepted Answer

A table that shows how data are partitioned among several categories by listing the categories along with the number (frequency) of data values in each.

Question 2

How is the class midpoint for a frequency distribution calculated?

Accepted Answer

By dividing the sum of the lower and upper class limits by 2: $$\frac{	ext{Lower class limit} + 	ext{Upper class limit}}{2}$$

Question 3

What is the class width if the lowest value in a data set is 12, the highest is 72, and you want 5 classes?

Accepted Answer

$$\frac{72 - 12}{5} = 12$$, rounded up to 15

Question 4

Which of the following statements about relative frequency distributions is TRUE?

Accepted Answer

Relative frequency is calculated by dividing the class frequency by the total number of data values.

Question 5

A cumulative frequency distribution is most useful for which of the following purposes?

Accepted Answer

Determining the number of data values less than or equal to a certain value.

Question 6

If a frequency distribution has frequencies that start low, increase to a maximum, and then decrease, and is approximately symmetric, what can you infer about the data?

Accepted Answer

The data are likely to have a normal distribution.

Question 7

What does the presence of a large gap in a frequency distribution suggest?

Accepted Answer

The data may come from two or more different populations.

Question 8

Which of the following is the correct formula for class width?

Accepted Answer

$$	ext{Class width} = 	ext{Difference between two consecutive lower class limits}$$

Question 9

Suppose you are comparing the relative frequency distributions of commute times in two cities. City A has 80% of commutes under 30 minutes, while City B has only 30% under 30 minutes. What can you conclude?

Accepted Answer

City A has a higher proportion of short commutes.

Question 10

Which of the following is NOT a step in constructing a frequency distribution?

Accepted Answer

Calculate the mean and median of the data.

Question 11

If the lower class limits of a frequency distribution are 0, 10, 20, 30, and 40, what is the class width?

Accepted Answer

$$10$$

Question 12

Why is it important to round up the class width when constructing a frequency distribution?

Accepted Answer

To ensure that all data values are included in the classes.

Question 13

Which of the following best describes class boundaries?

Accepted Answer

The values that separate classes without creating gaps.

Question 14

A frequency distribution for the weights of pennies shows a large gap between two groups of values. What is the most reasonable explanation?

Accepted Answer

The pennies come from two different populations, such as pre-1983 and post-1983 pennies.

Question 15

Which of the following is a critical use of frequency distributions in statistics?

Accepted Answer

To determine if the data are normally distributed.

Exploring Data with Tables and Graphs: Frequency Distributions and Data Visualization

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