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Chapter 2: Problem 12

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

Short Answer

Expert verified
Relative frequencies are calculated by dividing class frequencies by the total number of observations. This gives the proportion of data that falls within each class. To calculate percentages, simply multiply relative frequencies by 100. In the example, for a class with 25 observations in a data set of 100, the relative frequency would be 0.25 or 25%, calculated as (25/100)*100.

Step by step solution

01

Understanding Definitions

A class usually refers to a category within a variable. Class frequency refers to the number of observations that fall within a particular class. Relative frequency of a class is just the class frequency divided by the total number of observations in the dataset. So it provides the proportion of the data that falls within a certain class. Percentage is just the relative frequency multiply by 100.
02

Create a Hypothetical Data set

Let's suppose we have a data set of 100 students and their grades in a test. The grades are distributed as follows: Grade A: 25 students, Grade B: 30 students, Grade C: 20 students, Grade D: 15 students, Grade F: 10 students.
03

Calculate Relative Frequencies

To do this, divide the frequency of each grade by the total number of students. For example, the relative frequency of Grade A would be \( \frac{25}{100} = 0.25 \). Similarly, calculate the relative frequency for each grade.
04

Calculate Percentages

To convert relative frequencies into percentages, multiply each by 100. So the percentage of students with Grade A would be \( 0.25 \times 100 = 25\% \). Repeat this for each grade.

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Most popular questions from this chapter

Twenty-four students from universities in Connecticut were asked to name the five current members of the U.S. House of Representatives from Connecticut. The number of correct names supplied by the students are given below. $$ \begin{array}{llllllllllll} 4 & 2 & 3 & 5 & 5 & 4 & 3 & 1 & 5 & 4 & 4 & 3 \\ 5 & 3 & 2 & 3 & 1 & 3 & 2 & 5 & 2 & 1 & 5 & 0 \end{array} $$ a. Prepare a frequency distribution for these data using single-valued classes. b. Compute the relative frequency and percentage distributions. c. What percentage of the students in this sample named fewer than two of the representatives correctly? d. Draw a bar graph for the relative frequency distribution.

The following data give the amounts spent on video rentals (in dollars) during 2009 by 30 households randomly selected from those who rented videos in 2009. $$ \begin{array}{rrrrrrrrr} 595 & 24 & 6 & 100 & 100 & 40 & 622 & 405 & 90 \\ 55 & 155 & 760 & 405 & 90 & 205 & 70 & 180 & 88 \\ 808 & 100 & 240 & 127 & 83 & 310 & 350 & 160 & 22 \\ 111 & 70 & 15 & & & & & & \end{array} $$ a. Construct a frequency distribution table. Take \(\$ 1\) as the lower limit of the first class and \(\$ 200\) as the width of each class. b. Calculate the relative frequencies and percentages for all classes. c. What percentage of the households in this sample spent more than \(\$ 400\) on video rentals in \(2009 ?\)

Why do we need to group data in the form of a frequency table? Explain briefly.

The following data give the results of a sample survey. The letters \(\mathrm{A}, \mathrm{B}\), and \(\mathrm{C}\) represent the three categories. $$ \begin{array}{llllllllll} \text { A } & \text { B } & \text { B } & \text { A } & \text { C } & \text { B } & \text { C } & \text { C } & \text { C } & \text { A } \\ \text { C } & \text { B } & \text { C } & \text { A } & \text { C } & \text { C } & \text { B } & \text { C } & \text { C } & \text { A } \\ \text { A } & \text { B } & \text { C } & \text { C } & \text { B } & \text { C } & \text { B } & \text { A } & \text { C } & \text { A } \end{array} $$ a. Prepare a frequency distribution table. b. Calculate the relative frequencies and percentages for all categories. c. What percentage of the elements in this sample belong to category \(\mathrm{B}\) ? d. What percentage of the elements in this sample belong to category \(\mathrm{A}\) or \(\mathrm{C}\) ? e. Draw a bar graph for the frequency distribution.

The following data give the numbers of computer keyboards assembled at the Twentieth Century Electronics Company for a sample of 25 days. $$ \begin{array}{lllllllllllll} 45 & 52 & 48 & 41 & 56 & 46 & 44 & 42 & 48 & 53 & 51 & 53 & 51 \\ 48 & 46 & 43 & 52 & 50 & 54 & 47 & 44 & 47 & 50 & 49 & 52 & \end{array} $$ a. Make the frequency distribution table for these data. b. Calculate the relative frequencies for all classes. c. Construct a histogram for the relative frequency distribution. d. Construct a polygon for the relative frequency distribution.
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