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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 involved in constructing a frequency distribution table are determining the number of classes, deciding on the class width, and establishing the class limits.

Step by step solution

01

Decision on Number of Classes

The first decision to be made when constructing a frequency distribution table is the number of classes or groups to include. Generally, this decision is made based on the data set size and the level of detail needed for the analysis. Too many or too few classes can hinder the analysis of the data. A common rule of thumb is to have between 5 and 20 classes.
02

Determining the Class Width

The second decision involves determining the width of the classes. This is the range of data values that each class will contain. This decision depends on the spread of data in the data set. To compute class width, subtract the smallest data value from the largest and divide by the number of classes. The class width should generally be a simple number that facilitates easy data categorization and interpretation.
03

Establishing Class Limits

The third decision is about establishing the class limits. These limits define the data range included in each class and are important in avoiding data overlap between classes. The lower limit of a class is the smallest data value it can include, and the upper limit is the highest value. Typically, in a frequency distribution table, the class limits are clearly stated to ensure the data's proper categorization.

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Most popular questions from this chapter

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

Refer to Exercise 2.19, which contains data on the birth rates for all 56 counties of Montana for the year 2008 . Here are the data rounded to the nearest unit: \(\begin{array}{rrrrrrrr}10 & 22 & 16 & 12 & 8 & 3 & 15 & 8 \\ 14 & 9 & 11 & 9 & 15 & 10 & 14 & 15 \\ 18 & 23 & 5 & 6 & 20 & 8 & 10 & 15 \\ 14 & 10 & 10 & 10 & 9 & 9 & 14 & 12 \\ 11 & 11 & 2 & 10 & 11 & 5 & 7 & 9 \\ 10 & 14 & 20 & 19 & 11 & 7 & 12 & 12 \\ 11 & 9 & 8 & 7 & 10 & 10 & 6 & 15\end{array}\) a. Prepare a stem-and-leaf display for the data. Arrange the leaves for each stem in increasing order. b. Prepare a split stem-and-leaf display for the data. Split each stem into two parts. The first part should contains the leaves \(0,1,2,3\), and 4, and the second part should contains the leaves 5,6 , 7,8, and \(9 .\) c. Which display (the one in part a or the one in part b) provides a better representation of the features of the distribution? Explain why you believe this.

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 \(7-9\).

Refer to Exercise \(2.21\), which contains data on the amount of money donated to charity by the top 40 donors in the 2010 Slate 60 . Here are the amounts rounded to the nearest million dollars. \(\begin{array}{rrrrrrrrrr}332 & 279 & 163 & 120 & 118 & 117 & 110 & 101 & 101 & 100 \\ 100 & 88 & 84 & 80 & 67 & 62 & 59 & 53 & 50 & 50 \\\ 50 & 50 & 49 & 45 & 42 & 41 & 40 & 39 & 35 & 33 \\ 32 & 32 & 30 & 30 & 30 & 30 & 30 & 29 & 28 & 27\end{array}\) a. Prepare a stem-and-leaf display for the data. The stems should consist of the hundreds digits, and the leaves should consist of the tens and ones digits (e.g., for the number 117 , the stem would be 1 and the leaf would be 17 , while for the number 41 , the stem would be 0 and the leaf would be 41 ). Arrange the leaves for each stem in increasing order. b. Prepare a split stem-and-leaf display for the data. Split each stem into two parts. The first part should contain the leaves with \(0,1,2,3\), and 4 in the tens place, and the second part should contains the leaves with \(5,6,7,8\), and 9 in the tens place. c. Which display (the one in part a or the one in part b) provides a better representation of the features of the distribution? Explain why you believe this.

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