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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 number of turnovers (fumbles and interceptions) made by both teams in each of the football games played by North Carolina State University during the 2009 and 2010 seasons. $$ \begin{array}{llllllllllll} 2 & 3 & 1 & 1 & 6 & 5 & 3 & 5 & 5 & 1 & 5 & 2 \\ 5 & 3 & 4 & 4 & 5 & 8 & 4 & 5 & 2 & 2 & 2 & 6 \end{array} $$ 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 games in which there were 4 or 5 turnovers? d. Draw a bar graph for the frequency distribution of part a.

The following data give the money (in dollars) spent on textbooks by 35 students during the \(2011-12\) academic year. \(\begin{array}{lllllllll}565 & 728 & 870 & 620 & 345 & 868 & 610 & 765 & 550 \\ 845 & 530 & 705 & 490 & 258 & 320 & 505 & 957 & 787 \\ 617 & 721 & 635 & 438 & 575 & 702 & 538 & 720 & 460 \\ 840 & 890 & 560 & 570 & 706 & 430 & 968 & 638 & \end{array}\) a. Prepare a stem-and-leaf display for these data using the last two digits as leaves. b. Condense the stem-and-leaf display by grouping the stems as \(2-4,5-6\), and \(7-9\).

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.

Consider the following stem-and-leaf display. $$ \begin{array}{l|lllllll} 4 & 3 & 6 & & & & & & \\ 5 & 0 & 1 & 4 & 5 & & & & \\ 6 & 3 & 4 & 6 & 7 & 7 & 7 & 8 & 9 \\ 7 & 2 & 2 & 3 & 5 & 6 & 6 & 9 & \\ 8 & 0 & 7 & 8 & 9 & & & & \end{array} $$ Write the data set that is represented by this display.

The following data give the number of text messages sent on 40 randomly selected days during 2012 by a high school student: \(\begin{array}{llllllllll}32 & 33 & 33 & 34 & 35 & 36 & 37 & 37 & 37 & 37 \\\ 38 & 39 & 40 & 41 & 41 & 42 & 42 & 42 & 43 & 44 \\ 44 & 45 & 45 & 45 & 47 & 47 & 47 & 47 & 47 & 48 \\ 48 & 49 & 50 & 50 & 51 & 52 & 53 & 54 & 59 & 61\end{array}\) a. Construct a frequency distribution table. Take 32 as the lower limit of the first class and 6 as the class width. b. Calculate the relative frequency and percentage for each class. c. Construct a histogram for the frequency distribution of part a. d. On what percentage of these 40 days did this student send more than 44 text messages?
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