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Chapter 2: Problem 11

Briefly explain the three decisions that have to be made to group a data set in the form of a frequency distribution table.

Short Answer

Expert verified
The three decisions for creating a frequency distribution table include: Determining the number of classes (usually around \( \sqrt{n} \)), Deciding on the class intervals (typically equalling size across classes, with interval size calculated as \( \frac{{range of data}}{{number of classes}} \)), and Counting the class frequency i.e, the number of data points in each class.

Step by step solution

01

Decision 1 - Number of Classes

One must decide the number of classes or groups. The choice depends on the size and spread of the data. This number usually ranges from 5 to 20. A common practice is to choose a number around \( \sqrt{n} \) where n is the number of data points.
02

Decision 2 - Class Intervals

Determine the class intervals. Here, the goal is to size each class so that it covers a range of data values. Typically, the intervals are chosen so all have the same size. The size of the interval could be calculated as \( \frac{{range of data}}{{number of classes}} \). This, however, 鈭� for skewed or irregularly distributed data, unequal class intervals can be used.
03

Decision 3 - Class Frequencies

Lastly, count the frequency for each class which is the number of data items falling within that class. This is done by going through the data set and categorizing each data point into its respective class.

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Most popular questions from this chapter

A sample of 80 adults was taken, and these adults were asked about the number of credit cards they possess. The following table gives the frequency distribution of their responses. $$ \begin{array}{lc} \hline \text { Number of Credit Cards } & \text { Number of Adults } \\ \hline 0 \text { to } 3 & 18 \\ 4 \text { to } 7 & 26 \\ 8 \text { to } 11 & 22 \\ 12 \text { to } 15 & 11 \\ 16 \text { to } 19 & 3 \\ \hline \end{array} $$ a. Find the class boundaries and class midpoints. b. Do all classes have the same width? If so, what is this width? c. Prepare the relative frequency and percentage distribution columns. d. What percentage of these adults possess 8 or more credit cards?

Briefly explain the concept of cumulative frequency distribution. How are the cumulative relative frequencies and cumulative percentages calculated?

The following table lists the average price per gallon for unleaded regular gasoline in the United States from 1999 to 2008 . $$ \begin{array}{lc} \hline \text { Year } & \begin{array}{c} \text { Average Price per Gallon } \\ \text { (dollars) } \end{array} \\ \hline 1999 & 1.136 \\ 2000 & 1.484 \\ 2001 & 1.420 \\ 2002 & 1.345 \\ 2003 & 1.561 \\ 2004 & 1.852 \\ 2005 & 2.270 \\ 2006 & 2.572 \\ 2007 & 2.796 \\ 2008 & 3.246 \\ \hline \end{array} $$ Draw two bar graphs for these data-the first without truncating the axis on which price is marked, and the second by truncating this axis. In the second graph, mark the prices on the vertical axis starting with $$\$ 1.00 .$$ Briefly comment on the two bar graphs.

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

The following table, reproduced from Exercise 2.15, gives the frequency distribution of ages for all 50 employees of a company. $$ \begin{array}{lc} \hline \text { Age } & \text { Number of Employees } \\ \hline 18 \text { to } 30 & 12 \\ 31 \text { to } 43 & 19 \\ 44 \text { to } 56 & 14 \\ 57 \text { to } 69 & 5 \\ \hline \end{array} $$ a. Prepare a cumulative frequency distribution table. b. Calculate the cumulative relative frequencies and cumulative percentages for all classes. c. What percentage of the employees of this company are 44 years of age or older? d. Draw an ogive for the cumulative percentage distribution. e. Using the ogive, find the percentage of employees who are age 40 or younger.
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