Question 1

Which of the following best describes the purpose of a frequency distribution in statistics?

Accepted Answer

To organize raw data into classes or intervals and show the count of data entries in each class.

Question 2

Given a data set with a minimum value of 22 and a maximum value of 97, and you are asked to create 8 classes, what is the appropriate class width? (Round up to the next whole number.)

Accepted Answer

$$ \frac{97-22}{8} = 9.375 $$, so class width is 10

Question 3

What is the formula for the midpoint of a class with lower class limit $$L$$ and upper class limit $$U$$?

Accepted Answer

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

Question 4

A frequency distribution has the following classes: 10-19, 20-29, 30-39. What is the class boundary between the first and second class?

Accepted Answer

$$ 19.5 $$

Question 5

If a class in a frequency table has a frequency of 8 and the total sample size is 40, what is the relative frequency of that class?

Accepted Answer

$$ \frac{8}{40} = 0.2 $$

Question 6

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

Accepted Answer

Bars are separated by gaps to show different categories.

Question 7

What is the cumulative frequency for the third class if the frequencies for the first three classes are 4, 7, and 9?

Accepted Answer

$$ 4 + 7 + 9 = 20 $$

Question 8

Why are class boundaries used instead of class limits when constructing a histogram?

Accepted Answer

To ensure that the bars in the histogram touch each other without gaps.

Question 9

A cumulative frequency ogive is most useful for which of the following tasks?

Accepted Answer

Determining the proportion of data values below a certain value.

Question 10

Which of the following graphs is best for displaying the continuous change in frequencies across class midpoints?

Accepted Answer

Frequency polygon

Question 11

Suppose you have the following class limits: 50-59, 60-69, 70-79. What is the lower boundary of the first class?

Accepted Answer

$$ 49.5 $$

Question 12

If the range of a data set is 72 and you want 9 classes, what is the class width?

Accepted Answer

$$ \frac{72}{9} = 8 $$

Question 13

Which of the following is a correct interpretation of a relative frequency histogram?

Accepted Answer

It shows the percentage of data values in each class.

Question 14

A data set has the following frequencies for its classes: 2, 5, 8, 3, 2. What is the cumulative frequency for the fourth class?

Accepted Answer

$$ 2 + 5 + 8 + 3 = 18 $$

Question 15

Which of the following is a real-world application of an ogive?

Accepted Answer

Tracking cumulative rainfall over a season.

Question 16

If a frequency distribution has classes with the following lower limits: 10, 20, 30, 40, what is the class width?

Accepted Answer

$$ 10 $$

Question 17

Which of the following statements about frequency polygons is TRUE?

Accepted Answer

They use class midpoints on the horizontal axis.

Question 18

A frequency table for exam scores has the following classes: 60-69, 70-79, 80-89. If 15 students scored between 70 and 79, and the total number of students is 50, what is the relative frequency for the 70-79 class?

Accepted Answer

$$ \frac{15}{50} = 0.3 $$

Descriptive Statistics: Frequency Distributions and Their Graphs

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