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Chapter 2: Problem 1

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

Short Answer

Expert verified
We need to group data in the form of a frequency table to organise and represent it in a way that is easier to handle and interpret. It allows us to see how often certain values occur, which helps in finding patterns and trends in data. They simplify large chunks of data and lay foundation for many statistical analyses.

Step by step solution

01

Understanding what a Frequency Table is

A frequency table is a way to organise and represent data. It allows you to group the data into categories and record the frequency of each category. It involves dividing the range of the data into classes and counting how many data points fall into each subclass.
02

Functions of Frequency Tables

Frequency tables provide a detailed view of the data, which is very useful especially when dealing with large amounts of information. They make it easier to view and handle the data since it is organised. The concept of frequencies provides valuable information about how often certain data points or ranges of data points make an appearance.
03

Benefit of Frequency Tables

The benefit of frequency tables is that they provide a clear overview of the data, which makes it more comfortable to handle. They are great tools for finding patterns and trends in data. They simplify data, making it easier to interpret and understand. Moreover, they are the foundation for many statistical analyses.

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Most popular questions from this chapter

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 A or C? e. Draw a bar graph for the frequency distribution.

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?

Each state collects information on every birth that occurs within its borders. The following data give the 2008 birth rates (number of births per 1000 people) for all of the 56 counties in the state of Montana (http://www.dphhs.mt.gov/statisticalinformation/vitalstats/index.shtml). \(\begin{array}{rrrrrrrr}10.1 & 22.2 & 15.8 & 12.2 & 7.7 & 3.1 & 14.5 & 7.8 \\\ 13.6 & 8.8 & 10.9 & 8.9 & 14.7 & 9.6 & 14.2 & 14.9 \\ 18.3 & 22.8 & 5.4 & 5.6 & 19.6 & 8.2 & 9.9 & 14.7 \\ 13.7 & 10.3 & 9.7 & 9.8 & 8.6 & 9.4 & 14.1 & 12.3 \\ 10.5 & 11.4 & 2.2 & 9.8 & 10.9 & 4.6 & 6.6 & 8.5 \\ 10.2 & 14.4 & 20.4 & 18.5 & 10.8 & 6.5 & 11.6 & 12.1 \\ 10.5 & 9.3 & 8.1 & 7.4 & 10.2 & 9.7 & 5.6 & 14.5\end{array}\) a. Construct a frequency distribution table using the classes 2 to less than 5,5 to less than 8,8 to less than 11,11 to less than 14,14 to less than 17,17 to less than 20 , and 20 to less than 23 . b. Calculate the relative frequency and percentage for each class. c. Construct a histogram and a polygon for the birth-rate percentage distribution. d. What percentage of the counties had a birth rate of less than 11 births per 1000 people?

Suppose a data set contains the ages of 135 autoworkers ranging from 20 to 53 years. A. Using Sturge's formula given in footnote 1 in section \(2.2 .2\), find an appropriate number of classes for a frequency distribution for this data set. b. Find an appropriate class width based on the number of classes in part a.

Twenty-four patrons at a baseball game were observed in order to determine how many hot dogs each of them ate during the game. The following table contains the data. $$ \begin{array}{llllllllllll} 4 & 2 & 1 & 2 & 1 & 0 & 2 & 2 & 2 & 3 & 0 & 3 \\ 3 & 4 & 1 & 4 & 6 & 1 & 5 & 0 & 0 & 2 & 3 & 2 \end{array} $$ a. Construct a frequency distribution table for these data using single-valued classes. b. Calculate the relative frequency and percentage for each class. c. What is the relative frequency of patrons who ate fewer than 4 hot dogs? d. Draw a bar graph for the frequency distribution of part a.
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