Q: How is the class midpoint calculated for a class with lower class limit 15 and upper class limit 29?

$$\text{Class midpoint} = \frac{15 + 29}{2} = 22$$

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

Given a frequency distribution with lower class limits of 10, 20, 30, 40, and 50, what is the class width?

Accepted Answer

$$	ext{Class width} = 10$$

Question 3

How is the class midpoint calculated for a class with lower class limit 15 and upper class limit 29?

Accepted Answer

$$	ext{Class midpoint} = \frac{15 + 29}{2} = 22$$

Question 4

A frequency distribution for commute times in Los Angeles uses a class width of 15 minutes. If the first lower class limit is 0, what is the lower class limit for the fourth class?

Accepted Answer

$$0 + 3 	imes 15 = 45$$

Question 5

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

Accepted Answer

Each class frequency is replaced by a relative frequency or percentage, and the sum of percentages should be very close to 100%.

Question 6

If a cumulative frequency distribution has frequencies for classes as follows: 5, 12, 20, 28, 35, what is the cumulative frequency for the fourth class?

Accepted Answer

$$5 + 12 + 20 = 37$$

Question 7

A frequency distribution shows a large gap between two groups of data values. What does this gap most likely indicate?

Accepted Answer

The data are from two or more different populations.

Question 8

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

Accepted Answer

Determine the mean and standard deviation of the data.

Question 9

If the frequencies in a distribution start low, increase to a maximum, and then decrease symmetrically, what type of distribution is this?

Accepted Answer

A normal distribution

Question 10

Suppose you have a frequency distribution with lower class limits of 0, 15, 30, 45, 60, 75, and 90. What are the upper class limits if the class width is 15?

Accepted Answer

14, 29, 44, 59, 74, 89, 104

Question 11

Which of the following best describes class boundaries?

Accepted Answer

The numbers used to separate the classes, but without the gaps created by class limits.

Question 12

A frequency distribution for the weights of pennies shows a gap between the lightest and heaviest pennies. What is the most likely explanation for this gap?

Accepted Answer

Pennies were manufactured with different metal compositions before and after a certain year.

Question 13

If you are constructing a frequency distribution and the minimum value in your data set is 7, which of the following is a good choice for the first lower class limit?

Accepted Answer

A convenient value below the minimum, such as 0

Question 14

Which of the following is a critical insight when analyzing frequency distributions for normality?

Accepted Answer

Frequencies should start low, increase to a maximum, then decrease to low, and the distribution should be approximately symmetric.

Question 15

If a frequency distribution has class frequencies of 8, 12, 15, 10, and 5, what is the cumulative frequency for the third class?

Accepted Answer

$$8 + 12 + 15 = 35$$

Question 16

Which of the following is TRUE about gaps in a frequency distribution?

Accepted Answer

Gaps can indicate data from different populations, but data from different populations do not always result in gaps.

Question 17

A frequency distribution is constructed with 7 classes. If the range of the data is 84, what is the minimum class width you should use?

Accepted Answer

$$	ext{Class width} = \frac{84}{7} = 12 ($$rounded up to 15)

Question 18

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

Accepted Answer

$$	ext{Class width} = \frac{	ext{Range}}{	ext{Number of classes}}$$

Question 19

In constructing a frequency distribution, why is it recommended to round up the class width to a convenient number?

Accepted Answer

To ensure that all data values are included and classes are easy to interpret.

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

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