Q: Which of the following is a correct formula for calculating relative frequency?

$$ \text{Relative Frequency} = \frac{\text{Frequency of Category}}{\text{Total Number of Observations}} $$

Question 1

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

Accepted Answer

A table that lists each category of data and the number of occurrences for each category.

Question 2

Suppose a survey records the favorite ice cream flavor of 100 students. The data is organized into a table showing the number of students for each flavor. What type of data organization is this?

Accepted Answer

Qualitative frequency distribution

Question 3

If a category in a frequency distribution has 45 observations out of a total of 100, what is the relative frequency of this category?

Accepted Answer

$$ \frac{45}{100} = 0.45 $$

Question 4

Which of the following statements about cumulative frequency is correct?

Accepted Answer

It is the sum of all frequencies up to and including a given category.

Question 5

A frequency distribution table for survey responses is shown below:

- Yes: 30
- No: 50
- Maybe: 20

What is the relative frequency for 'No'?

Accepted Answer

$$ \frac{50}{100} = 0.5 $$

Question 6

In a cumulative frequency table, the cumulative frequency for the third category is 75. If the frequencies for the first and second categories are 30 and 25 respectively, what is the frequency for the third category?

Accepted Answer

$$ 75 - (30 + 25) = 20 $$

Question 7

Why is it important to use relative frequency instead of absolute frequency when comparing categories in datasets of different sizes?

Accepted Answer

Relative frequency standardizes the data, allowing for meaningful comparisons across datasets of different sizes.

Question 8

A researcher organizes survey responses into a frequency distribution and then sorts the categories in decreasing order of frequency. What is the main purpose of this step?

Accepted Answer

To highlight the most common categories and facilitate data interpretation.

Question 9

Given the following frequency distribution for favorite colors among 80 students:

- Red: 20
- Blue: 30
- Green: 15
- Yellow: 15

What is the cumulative frequency after the 'Green' category?

Accepted Answer

$$ 20 + 30 + 15 = 65 $$

Question 10

A frequency distribution table is constructed for a set of qualitative data. Which of the following is NOT a valid step in this process?

Accepted Answer

Calculating the mean of the categories.

Question 11

If the relative frequency of a category is 0.25 in a dataset of 200 observations, how many times does this category occur?

Accepted Answer

$$ 0.25 	imes 200 = 50 $$

Question 12

Which of the following best describes the difference between frequency and relative frequency?

Accepted Answer

Frequency is the count of occurrences, while relative frequency is the proportion of occurrences out of the total.

Question 13

A hospital records the blood types of 500 patients. The frequency distribution shows:

- Type A: 200
- Type B: 150
- Type AB: 50
- Type O: 100

What is the relative frequency of Type O?

Accepted Answer

$$ \frac{100}{500} = 0.2 $$

Question 14

In a frequency distribution, what does sorting categories in decreasing order of frequency help achieve?

Accepted Answer

It makes it easier to identify the most common categories.

Question 15

A class survey asks students about their preferred study method. The results are:

- Group study: 12
- Solo study: 18
- Online resources: 10

What is the cumulative frequency after 'Solo study'?

Accepted Answer

$$ 12 + 18 = 30 $$

Question 16

If a frequency distribution has the following relative frequencies: 0.3, 0.4, and 0.3, what is the total number of observations if the frequency for the first category is 60?

Accepted Answer

$$ \frac{60}{0.3} = 200 $$

Question 17

Which of the following is a correct formula for calculating relative frequency?

Accepted Answer

$$ 	ext{Relative Frequency} = \frac{	ext{Frequency of Category}}{	ext{Total Number of Observations}} $$

Question 18

A frequency distribution for a survey on favorite sports is as follows:

- Soccer: 40
- Basketball: 35
- Tennis: 25

If the total number of responses is 100, what is the relative frequency for Tennis?

Accepted Answer

$$ \frac{25}{100} = 0.25 $$

Question 19

A frequency distribution table is constructed for a set of survey responses. What is the first step in creating this table?

Accepted Answer

List all categories and count the number of occurrences for each.

Qualitative Data Organization and Frequency Distributions in Statistics

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