Q: A class in a frequency distribution has a frequency of 12 out of a total of 60 data values. What is the percentage for this class?

$$\frac{12}{60} \times 100 = 20\%$$

Question 1

A researcher collects the weights (in grams) of 100 apples and wants to organize the data into a frequency distribution. The weights range from 120g to 220g. If she wants to use 5 classes, what is the appropriate class width to use?

Accepted Answer

$$\frac{220 - 120}{5} = 20$$

Question 2

Which of the following best describes a relative frequency distribution?

Accepted Answer

A table that lists each class with the proportion or percentage of data values in each class.

Question 3

Suppose you are constructing a frequency distribution for the number of hours students study per week, and the data are continuous and expressed as decimals. Which grouping method should you use?

Accepted Answer

Cutpoint grouping

Question 4

Given the following class limits for a frequency distribution: 10-19, 20-29, 30-39, what is the class width?

Accepted Answer

$$20 - 10 = 10$$

Question 5

A frequency distribution for the weights of coins shows a large gap between two groups of weights. What is the most likely explanation for this gap?

Accepted Answer

The data are from two different populations, such as coins made from different materials.

Question 6

If the frequencies in a frequency distribution start low, increase to a maximum, and then decrease to low frequencies, what can you infer about the shape of the distribution?

Accepted Answer

It is approximately symmetric and possibly normal.

Question 7

How do you calculate the class midpoint (class mark) for a class with lower class limit $$L$$ and upper class limit $$U$$?

Accepted Answer

$$\frac{L + U}{2}$$

Question 8

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

Accepted Answer

Determining the proportion of data values below a certain value.

Question 9

A class in a frequency distribution has a frequency of 8, and the total number of data values is 40. What is the relative frequency for this class?

Accepted Answer

$$\frac{8}{40} = 0.20$$

Question 10

When 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 in the classes without overlap.

Question 11

In a frequency distribution, what is the purpose of class boundaries?

Accepted Answer

To separate classes without gaps created by class limits.

Question 12

A hospital administrator wants to compare the waiting times at two different clinics. Which type of frequency distribution would best facilitate this comparison?

Accepted Answer

A relative frequency distribution for both clinics in the same table.

Question 13

If a frequency distribution for exam scores has the following frequencies: 2, 5, 8, 5, 2, what is the likely shape of the distribution?

Accepted Answer

Approximately symmetric

Question 14

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

Accepted Answer

Assign data values to classes before determining class limits.

Question 15

A data set of cholesterol levels is grouped into classes with lower class limits of 150, 160, 170, 180, and 190. What is the class width?

Accepted Answer

$$160 - 150 = 10$$

Question 16

If the sum of the relative frequencies in a distribution is 0.98, what is the most likely explanation?

Accepted Answer

The sum is less than 1 due to rounding errors.

Question 17

A class in a frequency distribution has a frequency of 12 out of a total of 60 data values. What is the percentage for this class?

Accepted Answer

$$\frac{12}{60} 	imes 100 = 20\%$$

Question 18

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

Accepted Answer

Gaps may indicate data from two or more different populations.

Question 19

A teacher wants to summarize the number of books read by students in a semester. The data are discrete and range from 0 to 6 books. Which grouping method is most appropriate?

Accepted Answer

Single-value grouping

Question 20

If a frequency distribution has class limits 50-59, 60-69, 70-79, what is the class midpoint for the class 60-69?

Accepted Answer

$$\frac{60 + 69}{2} = 64.5$$

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

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