Q: Which formula would you use to estimate the class width for a histogram?

$$\text{Width} \approx \frac{\text{Max} - \text{Min}}{\text{Number of Classes}}$$

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

Given the following frequencies for types of rehabilitation: Back (12), Wrist (2), Elbow (1), Hip (2), Shoulder (4), Knee (5), Hand (2), Groin (1), Neck (1), what is the relative frequency for 'Shoulder'? Use the formula $$	ext{Relative Frequency} = \frac{	ext{Frequency}}{	ext{Sum of all frequencies}}.$$

Accepted Answer

$$\frac{4}{30} = 0.1333$$

Question 3

Which type of chart would be most appropriate to visually compare the relative frequencies of different categories in a dataset?

Accepted Answer

Pie chart

Question 4

A physical therapist wants to display the number of patients needing rehabilitation for each body part. Which visual display is most appropriate?

Accepted Answer

Bar chart

Question 5

What is the main difference between a bar chart and a Pareto chart?

Accepted Answer

A Pareto chart arranges the bars in decreasing order of frequency or relative frequency.

Question 6

Which of the following is NOT a guideline for making good visual displays of data?

Accepted Answer

Use three-dimensional charts to make the data more visually appealing.

Question 7

A histogram is best used for which type of data?

Accepted Answer

Quantitative data

Question 8

If a histogram has a long tail to the right, how is the distribution described?

Accepted Answer

Skewed right

Question 9

Which formula would you use to estimate the class width for a histogram?

Accepted Answer

$$	ext{Width} \approx \frac{	ext{Max} - 	ext{Min}}{	ext{Number of Classes}}$$

Question 10

A dot plot is most useful for which of the following situations?

Accepted Answer

Displaying the distribution of a small set of discrete data

Question 11

Which of the following is a potential problem with using a truncated axis in a bar chart?

Accepted Answer

It can exaggerate differences between categories.

Question 12

Which of the following best describes a bell-shaped distribution?

Accepted Answer

The highest frequency occurs in the middle and frequencies decrease symmetrically on both sides.

Question 13

A stem-and-leaf plot is created for the following data: 147, 152, 153. What is the stem and leaf for 147?

Accepted Answer

Stem: 14, Leaf: 7

Question 14

Which of the following is a reason to avoid using 3D charts in data visualization?

Accepted Answer

They can distract the reader and lead to misinterpretation.

Question 15

A group of people were asked how many children they want to have. The histogram of their responses is heavily skewed to the right. What does this indicate about the data?

Accepted Answer

Most people want fewer children, with a few wanting many children.

Question 16

Which of the following is NOT a characteristic of a good frequency distribution for quantitative data?

Accepted Answer

Each class has a different width.

Question 17

If a pie chart shows that 40% of patients require back rehabilitation, how many out of 30 patients does this represent?

Accepted Answer

$$0.40 	imes 30 = 12$$

Question 18

Which of the following is a misleading practice when creating a bar chart?

Accepted Answer

Using bars of different widths for each category.

Question 19

A dataset is organized into classes with the following lower and upper limits: 10-19, 20-29, 30-39. What is the class width?

Accepted Answer

$$	ext{Class width} = 20 - 10 = 10$$

Organizing and Summarizing Data: Frequency Distributions and Graphical Displays

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