Q: A class midpoint is calculated using which formula?

$$ \text{Class midpoint} = \frac{\text{lower class limit} + \text{upper class limit}}{2} $$

Question 1

Which of the following best describes a frequency distribution?

Accepted Answer

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

Question 2

Suppose you are given the following commute times (in minutes) for a sample of 50 people: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50. If you want to create a frequency distribution with 5 classes, what is the appropriate class width? Use the formula $$ 	ext{Class width} = \frac{	ext{maximum data value} - 	ext{minimum data value}}{	ext{number of classes}} $$ and round up to the next whole number.

Accepted Answer

$$ \frac{50 - 5}{5} = 9 $$, so the class width is 10.

Question 3

What is the main difference between a frequency distribution and a relative frequency distribution?

Accepted Answer

A frequency distribution lists the counts for each class, while a relative frequency distribution lists the proportion or percentage of the total for each class.

Question 4

A researcher wants to summarize the number of hours students study per week. The data are: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20. If the lowest class limit is 0 and the class width is 5, what are the lower class limits for the first three classes?

Accepted Answer

0, 5, 10

Question 5

Which of the following is NOT a characteristic of a histogram?

Accepted Answer

Bars are separated by spaces to emphasize the differences between categories.

Question 6

Given the following frequency table for test scores: 50-59: 2, 60-69: 5, 70-79: 8, 80-89: 10, 90-99: 5. What is the relative frequency for the 80-89 class? Use $$ 	ext{Relative frequency} = \frac{	ext{frequency for a class}}{	ext{sum of all frequencies}} .$$

Accepted Answer

$$ \frac{10}{30} = 0.33 $$

Question 7

In constructing a frequency distribution, why is it important that classes do not overlap?

Accepted Answer

To ensure that each data value is counted in only one class.

Question 8

A class midpoint is calculated using which formula?

Accepted Answer

$$ 	ext{Class midpoint} = \frac{	ext{lower class limit} + 	ext{upper class limit}}{2} $$

Question 9

If a frequency distribution is approximately symmetric and the frequencies increase to a maximum and then decrease, what type of distribution does this suggest?

Accepted Answer

Normal distribution

Question 10

A bar graph is most appropriate for which type of variable?

Accepted Answer

Categorical variable

Question 11

A frequency distribution for commute times (in minutes) is constructed with the following lower class limits: 0, 15, 30, 45, 60. If the class width is 15, what is the upper class limit for the third class?

Accepted Answer

44

Question 12

Which of the following statements about cumulative frequency is correct?

Accepted Answer

Cumulative frequency for a class is the sum of the frequencies for that class and all previous classes.

Question 13

A student is constructing a histogram for the heights of 100 basketball players. Which axis should represent the class intervals?

Accepted Answer

The horizontal axis (x-axis)

Question 14

If the class boundaries for a class are 19.5 and 29.5, what is the class width?

Accepted Answer

$$ 29.5 - 19.5 = 10 $$

Question 15

Which of the following is a correct step in constructing a frequency distribution for quantitative data?

Accepted Answer

Select the number of classes, usually between 5 and 20.

Question 16

A relative frequency histogram differs from a frequency histogram in that:

Accepted Answer

The vertical axis represents relative frequencies instead of raw frequencies.

Question 17

If a frequency distribution has a class with a much higher frequency than the others, what effect will this have on the shape of the histogram?

Accepted Answer

The histogram will have a tall bar for that class, possibly indicating a mode.

Question 18

A frequency table for the number of pets owned by students is being constructed. The data are: 0, 1, 2, 2, 3, 3, 3, 4, 4, 5. What is the frequency for the class '3'?

Accepted Answer

3

Question 19

Which of the following best describes the purpose of using frequency distributions and histograms in real-world scenarios, such as analyzing commute times in a city?

Accepted Answer

They help to organize, summarize, and visualize large data sets to identify patterns and trends.

Frequency Distributions and Histograms: Study Notes

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