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Understanding Basic Statistics

8th Edition
Charles Henry Brase + 1 other
ISBN: 9781337558075

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BuyFindarrow_forward

Understanding Basic Statistics

8th Edition
Charles Henry Brase + 1 other
ISBN: 9781337558075
Textbook Problem

Political Science: Georgia Democrats How Democratic is Georgia? County-by-county results are shown for a recent election. For your convenience. the data have been sorted in increasing order (Source: Countyand City Data Book. 12th edition. U.S. Census Bureau).

Percentage of Democratic Vote by Counties in Georgia

31 33 34 34 35 35 35 36 38 38 38 39 40 40 40 40
41 41 41 41 41 41 41 42 42 43 44 44 44 45 45 46
46 46 46 47 48 49 49 49 49 50 51 52 52 53 53 53
53 53 55 56 56 57 57 59 62 66 66 68

(a) Make a bos-and-whisker plot of the data. Find the interquartile range.

(b) Grouped Data Make a frequency table using five classes. Then estimate the mean and sample standard deviation using the frequency table. Compute a 75% Chebyshev interval centered about the mean.

(c) If you have a statistical calculator or computer, use it to find the actual sample mean and sample standard deviation. Otherwise, use the values x = 2769  and  x 2 = 132 , 179 to compute the sample mean and sample standard deviation.

(a)

To determine

To graph: The box-and-whisker plot and interquartile range for the data.

Explanation

Graph: To create box-and-whisker plot by using MINITAB, the steps are as follows:

Step 1: Enter data in C1 of MINITAB worksheet.

Step 2: Go to Graph > Boxplot > Simple and click on OK.

Step 3: Enter C1 in dialog box of Graph variable.

Step 4: Click on OK.

The box-and-whisker plot is obtained as:

Calculation: Interquartile range (IQR) is simply the difference between the third and first quartiles. It is calculated by using Interquartile range=Q3Q1

First order the data from smallest to largest.

The lowest value in the data is 31 and highest value in the data is 68.

Next, find the median. Since the number of data values is 60, there is an even number of data, and the median is average of the 30th and 31th value. median=45+452=45

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