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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

Statisticians often need to know the shape of a population to make inferences. Suppose that you are asked to specify the shape of the population of weights of all college students. a. Sketch a graph of what you think the weights of all college students would look like. b. The following data give the weights (in pounds) of a random sample of 44 college students (F and M indicate female and male, respectively). $$ \begin{array}{llllllll} 123 \mathrm{~F} & 195 \mathrm{M} & 138 \mathrm{M} & 115 \mathrm{~F} & 179 \mathrm{M} & 119 \mathrm{~F} & 148 \mathrm{~F} & 147 \mathrm{~F} \\ 180 \mathrm{M} & 146 \mathrm{~F} & 179 \mathrm{M} & 189 \mathrm{M} & 175 \mathrm{M} & 108 \mathrm{~F} & 193 \mathrm{M} & 114 \mathrm{~F} \\ 179 \mathrm{M} & 147 \mathrm{M} & 108 \mathrm{~F} & 128 \mathrm{~F} & 164 \mathrm{~F} & 174 \mathrm{M} & 128 \mathrm{~F} & 159 \mathrm{M} \\ 193 \mathrm{M} & 204 \mathrm{M} & 125 \mathrm{~F} & 133 \mathrm{~F} & 115 \mathrm{~F} & 168 \mathrm{M} & 123 \mathrm{~F} & 183 \mathrm{M} \\ 116 \mathrm{~F} & 182 \mathrm{M} & 174 \mathrm{M} & 102 \mathrm{~F} & 123 \mathrm{~F} & 99 \mathrm{~F} & 161 \mathrm{M} & 162 \mathrm{M} \\ 155 \mathrm{~F} & 202 \mathrm{M} & 110 \mathrm{~F} & 132 \mathrm{M} & & & & \end{array} $$ i. Construct a stem-and-leaf display for these data. ii. Can you explain why these data appear the way they do? c. Now sketch a new graph of what you think the weights of all college students look like. Is this similar to your sketch in part a?

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.

The following data give the number of times each of the 30 randomly selected account holders at a bank used that bank's ATM during a 60 -day period. $$ \begin{array}{llllllllll} 3 & 2 & 3 & 2 & 2 & 5 & 0 & 4 & 1 & 3 \\ 2 & 3 & 3 & 5 & 9 & 0 & 3 & 2 & 2 & 15 \\ 1 & 3 & 2 & 7 & 9 & 3 & 0 & 4 & 2 & 2 \end{array} $$ Create a dotplot for these data and point out any clusters or outliers.

Nixon Corporation manufactures computer monitors. The following data are the numbers of computer monitors produced at the company for a sample of 30 davs. $$ \begin{array}{llllllllll} 24 & 32 & 27 & 23 & 33 & 33 & 29 & 25 & 23 & 28 \\ 21 & 26 & 31 & 22 & 27 & 33 & 27 & 23 & 28 & 29 \\ 31 & 35 & 34 & 22 & 26 & 28 & 23 & 35 & 31 & 27 \end{array} $$ a. Construct a frequency distribution table using the classes \(21-23,24-26,27-29,30-32\), and \(33-35\). b. Calculate the relative frequencies and percentages for all classes. c. Construct a histogram and a polygon for the percentage distribution. d. For what percentage of the days is the number of computer monitors produced in the interval \(27-29 ?\)

Thirty adults were asked which of the following conveniences they would find most difficult to do without: television (T), refrigerator (R), air conditioning (A), public transportation (P), or microwave (M). Their responses are listed below. $$ \begin{array}{cccccccccc} \mathrm{R} & \mathrm{A} & \mathrm{R} & \mathrm{P} & \mathrm{P} & \mathrm{T} & \mathrm{R} & \mathrm{M} & \mathrm{P} & \mathrm{A} \\ \mathrm{A} & \mathrm{R} & \mathrm{R} & \mathrm{T} & \mathrm{P} & \mathrm{P} & \mathrm{T} & \mathrm{R} & \mathrm{A} & \mathrm{A} \\ \mathrm{R} & \mathrm{P} & \mathrm{A} & \mathrm{T} & \mathrm{R} & \mathrm{P} & \mathrm{R} & \mathrm{A} & \mathrm{P} & \mathrm{R} \end{array} $$ a. Prepare a frequency distribution table. b. Calculate the relative frequencies and percentages for all categories. c. What percentage of these adults named refrigerator or air conditioning as the convenience that they would find most difficult to do without? d. Draw a bar graph for the relative frequency distribution.
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