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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

The following table gives the frequency distribution for the numbers of parking tickets received on the campus of a university during the past week for 200 students. $$ \begin{array}{cc} \hline \text { Number of Tickets } & \text { Number of Students } \\ \hline 0 & 59 \\ 1 & 44 \\ 2 & 37 \\ 3 & 32 \\ 4 & 28 \\ \hline \end{array} $$ Draw two bar graphs for these data, the first without truncating the frequency axis and the second by truncating the frequency axis. In the second case, mark the frequencies on the vertical axis starting with 25 . Briefly comment on the two bar graphs.

What is a stacked dotplot, and how is it used? Explain.

The accompanying table lists the 2006-07 median household incomes (rounded to the nearest dollar), for all 50 states and the District of Columbia. $$ \begin{array}{lccc} \hline \text { State } & \begin{array}{c} \text { 2006-07 Median } \\ \text { Household Income } \end{array} & \text { State } & \begin{array}{c} 2006-07 \text { Median } \\ \text { Household Income } \end{array} \\ \hline \text { AL } & 40,620 & \text { MT } & 42,963 \\ \text { AK } & 60,506 & \text { NE } & 49,342 \\ \text { AZ } & 47,598 & \text { NV } & 53,912 \\ \text { AR } & 39,452 & \text { NH } & 65,652 \\ \text { CA } & 56,311 & \text { NJ } & 65,249 \\ \text { CO } & 59,209 & \text { NM } & 42,760 \\ \text { CT } & 64,158 & \text { NY } & 49,267 \\ \text { DE } & 54,257 & \text { NC } & 42,219 \\ \text { D.C. } & 50,318 & \text { ND } & 44,708 \\ \text { FL } & 46,383 & \text { OH } & 48,151 \\ \text { GA } & 49,692 & \text { OK } & 41,578 \\ \text { HI } & 63,104 & \text { OR } & 49,331 \\ \text { ID } & 48,354 & \text { PA } & 49,145 \\ \text { IL } & 51,279 & \text { RI } & 54,735 \\ \text { IN } & 47,074 & \text { SC } & 42,477 \\ \text { IA } & 49,200 & \text { SD } & 46,567 \\ \text { KS } & 47,671 & \text { TN } & 41,521 \\ \text { KY } & 40,029 & \text { TX } & 45,294 \\ \text { LA } & 39,418 & \text { UT } & 54,853 \\ \text { ME } & 47,415 & \text { VT } & 50,423 \\ \text { MD } & 65,552 & \text { VA } & 58,950 \\ \text { MA } & 57,681 & \text { WA } & 57,178 \\ \text { MI } & 49,699 & \text { WV } & 40,800 \\ \text { MN } & 57,932 & \text { WI } & 52,218 \\ \text { MS } & 36,499 & \text { WY } & 48,560 \\ \text { MO } & 45,924 & & \\ \hline \end{array} $$ a. Construct a frequency distribution table. Use the following classes: \(36,000-40,999,41,000-\) \(45,999,46,000-50,999,51,000-55,999,56,000-60,999,61,000-65,999\) b. Calculate the relative frequencies and percentages for all classes. c. Based on the frequency distribution, can you say whether the data are symmetric or skewed? d. What percentage of these states had a median household income of less than \(\$ 56,000 ?\)

Create a dotplot for the following data set. $$ \begin{array}{llllllllll} 1 & 2 & 0 & 5 & 1 & 1 & 3 & 2 & 0 & 5 \\ 2 & 1 & 2 & 1 & 2 & 0 & 1 & 3 & 1 & 2 \end{array} $$

Three methods-writing classes using limits, using the less-than method, and grouping data using single-valued classes-were discussed to group quantitative data into classes. Explain these three methods and give one example of each.
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