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Chapter 2: Problem 2

How are the relative frequencies and percentages of categories obtained from the frequencies of categories? Illustrate with the help of an example.

Short Answer

Expert verified
Relative frequencies are calculated by dividing the frequency of each category by the total number of data points, and percentages are obtained by multiplying these relative frequencies by 100. For example, if five kids are asked about their favorite color and the results are: Blue (3 times), Green (once), and Red (once), then the relative frequencies are 0.6, 0.2, and 0.2 respectively while the percentages are 60%, 20%, and 20% respectively.

Step by step solution

01

Understanding the Terminology

Before starting with the calculations, you must understand what each term means: 鈥楩requency鈥� refers to how often a data point or category appears in a dataset. 鈥楻elative Frequency鈥� refers to the fraction of times a category occurs in the data set. 鈥楶ercentage鈥� is another way of expressing the relative frequency, but it's scaled to show the frequency out of 100.
02

Set Up an Example

Let's illustrate these concepts with an example where five kids are asked about their favorite color. Assume the results are: Blue, Green, Blue, Red, Blue.
03

Calculate Frequencies

Count the number of times each color is mentioned. The frequencies are: Blue = 3, Green = 1, Red = 1.
04

Calculate Relative Frequencies

To find the relative frequency, divide the frequency of each category by the total number of data points (in this case, the total number of kids). So the relative frequencies are: Blue = 3/5 = 0.6, Green = 1/5 = 0.2, Red = 1/5 = 0.2.
05

Calculate Percentages

To calculate percentages, multiply the relative frequencies by 100. So the percentages are: Blue = 0.6 * 100 = 60%, Green = 0.2 * 100 = 20%, Red = 0.2 * 100 = 20%.

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Most popular questions from this chapter

The following data give the numbers of television sets owned by 40 randomly selected households. \(\begin{array}{llllllllll}1 & 1 & 2 & 3 & 2 & 4 & 1 & 3 & 2 & 1 \\ 3 & 0 & 2 & 1 & 2 & 3 & 2 & 3 & 2 & 2 \\ 1 & 2 & 1 & 1 & 1 & 3 & 1 & 1 & 1 & 2 \\ 2 & 4 & 2 & 3 & 1 & 3 & 1 & 2 & 2 & 4\end{array}\) a. Prepare a frequency distribution table for these data using single-valued classes. b. Compute the relative frequency and percentage distributions. c. Draw a bar graph for the frequency distribution. d. What percentage of the households own two or more television sets?

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