Q: What is the formula for calculating the class width when organizing continuous data into classes?

$$\text{Class width} = \frac{\text{largest data value} - \text{smallest data value}}{\text{number of classes}}$$

Question 1

Which of the following best describes a frequency distribution?

Accepted Answer

A table that lists each category of data and the number of occurrences for each category.

Question 2

A physical therapist records the body part requiring rehabilitation for 30 patients. If 12 patients require back rehabilitation, what is the relative frequency for 'back'?

Accepted Answer

$$\frac{12}{30} = 0.4$$

Question 3

Which statement is TRUE about bar graphs and histograms?

Accepted Answer

Rectangles in histograms touch, but rectangles in bar graphs do not touch.

Question 4

What is the formula for calculating the class width when organizing continuous data into classes?

Accepted Answer

$$	ext{Class width} = \frac{	ext{largest data value} - 	ext{smallest data value}}{	ext{number of classes}}$$

Question 5

In a pie chart representing educational attainment, the degree measure for 'Not a high school graduate' is calculated as $$(0.0893) 	imes 360^\circ. $$What is the resulting angle?

Accepted Answer

$$32^\circ$$

Question 6

Why might a relative frequency graph be preferred over a frequency table when comparing data from two different years?

Accepted Answer

Relative frequency graphs allow for direct comparison of proportions, even if the total sample sizes differ.

Question 7

Which of the following is NOT a rule for constructing classes for continuous data?

Accepted Answer

Each observation should belong to more than one class.

Question 8

Given the following frequency distribution for arrivals at a restaurant: 1 customer (frequency 1), 2 customers (frequency 6), 3 customers (frequency 1), 4 customers (frequency 4), what is the relative frequency for 2 customers?

Accepted Answer

$$\frac{6}{40} = 0.15$$

Question 9

Which type of graph is best suited for displaying the distribution of a large set of continuous quantitative data?

Accepted Answer

Histogram

Question 10

A Pareto chart is a special type of bar graph. What distinguishes it from a standard bar graph?

Accepted Answer

Bars are drawn in decreasing order of frequency or relative frequency.

Question 11

If a data set consists of many different discrete values or is continuous, how should the categories (classes) be created?

Accepted Answer

By using intervals of numbers.

Question 12

Which of the following statements about frequency distributions is correct?

Accepted Answer

Frequency distributions can be constructed in different ways to best illustrate patterns in the data.

Question 13

In a histogram, what does the height of each rectangle represent?

Accepted Answer

The frequency or relative frequency of the class.

Question 14

Which of the following is a key difference between a pie chart and a bar chart?

Accepted Answer

A bar chart conveys more detailed data than a pie chart.

Question 15

If the relative frequency for a class is 0.25, what is the class percentage?

Accepted Answer

$$0.25 	imes 100 = 25\%$$

Question 16

A researcher wants to compare educational attainment in 1990 and 2021. Which graph would be most appropriate?

Accepted Answer

Side-by-side bar graph

Question 17

Which of the following is NOT a characteristic of classes for continuous data?

Accepted Answer

Classes should have unequal widths.

Question 18

Suppose you have a data set with a smallest value of 80, a largest value of 145, and you want 5 classes. What is the class width?

Accepted Answer

$$\frac{145 - 80}{5} = 13$$

Question 19

Which of the following best describes raw data?

Accepted Answer

Data collected from a survey or experiment that has not yet been organized.

Describing and Organizing Data: Frequency Distributions, Graphs, and Classes

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