Chapter03

Chapter 3 Graphical Methods for Describing Data

Frequency Distribution Example The data in the column labeled vision for the student data set introduced in the slides for chapter 1 is the answer to the question, “What is your principle means of correcting your vision?” The results are tabulated below

Bar Chart Examples This comparative bar chart is based on frequencies and it can be difficult to interpret and misleading. Would you mistakenly interpret this to mean that the females and males use contacts equally often? You shouldn’t. The picture is distorted because the frequencies of males and females are not equal.

Bar Chart Examples When the comparative bar chart is based on percents (or relative frequencies) (each group adds up to 100%) we can clearly see a difference in pattern for the eye correction proportions for each of the genders. Clearly for this sample of students, the proportion of female students with contacts is larger then the proportion of males with contacts.

Bar Chart Examples Stacking the bar chart can also show the difference in distribution of eye correction method. This graph clearly shows that the females have a higher proportion using contacts and both the no correction and glasses group have smaller proportions then for the males.

Pie Charts - Procedure ,[object Object],[object Object],[object Object],[object Object]

Pie Chart - Example ,[object Object]

Another Example This data constitutes the grades earned by the distance learning students during one term in the Winter of 2002.

Pie Chart – Another Example ,[object Object]

[object Object],Pie Chart – Another Example By pulling a slice (exploding) we can accentuate and make it clearing how A was the predominate grade for this course.

Stem and Leaf A quick technique for picturing the distributional pattern associated with numerical data is to create a picture called a stem-and-leaf diagram (Commonly called a stem plot). ,[object Object],[object Object],[object Object],[object Object]

Stem and Leaf Choosing the 1 st two digits as the stem and the 3 rd digit as the leaf we have the following 150 140 155 195 139 200 157 130 113 130 121 140 140 150 125 135 124 130 150 125 120 103 170 124 160 For our first example, we use the weights of the 25 female students. 10 11 12 13 14 15 16 17 18 19 20 3 3 154504 90050 000 05700 0 0 5 0

Stem and Leaf Typically we sort the order the stems in increasing order. We also note on the diagram the units for stems and leaves Stem: Tens and hundreds digits Leaf: Ones digit 10 11 12 13 14 15 16 17 18 19 20 3 3 014455 00059 000 00057 0 0 5 0 Probable outliers

Stem-and-leaf – GPA example The following are the GPAs for the 20 advisees of a faculty member. If the ones digit is used as the stem, you only get three groups. You can expand this a little by breaking up the stems by using each stem twice letting the 2 nd digits 0-4 go with the first and the 2 nd digits 5-9 with the second. The next slide gives two versions of the stem-and-leaf diagram. GPA 3.09 2.04 2.27 3.94 3.70 2.69 3.72 3.23 3.13 3.50 2.26 3.15 2.80 1.75 3.89 3.38 2.74 1.65 2.22 2.66

Stem-and-leaf – GPA example Stem: Ones digit Leaf: Tenths digits Note: The characters in a stem-and-leaf diagram must all have the same width, so if typing a fixed character width font such as courier. Stem: Ones digit Leaf: Tenths and hundredths digits 1L 1H 2L 2H 3L 3H 65,75 04,22,26,27 66,69,74,80 09,13,15,23,38 50,70,72,89,94 1L 1H 2L 2H 3L 3H 67 0222 6678 01123 57789

Comparative Stem and Leaf Diagram Student Weight (Comparing two groups) When it is desirable to compare two groups, back-to-back stem and leaf diagrams are useful. Here is the result from the student weights. From this comparative stem and leaf diagram, it is clear that the males weigh more (as a group not necessarily as individuals) than the females. 3 10 3 11 7 554410 12 145 95000 13 0004558 000 14 000000555 75000 15 0005556 0 16 00005558 0 17 000005555 18 0358 5 19 0 20 0 21 0 22 55 23 79

Comparative Stem and Leaf Diagram Student Age From this comparative stem and leaf diagram, it is clear that the male ages are all more closely grouped then the females. Also the females had a number of outliers. female male 7 1 9999 1 888889999999999999999 1111000 2 00000001111111111 3322222 2 2222223333 4 2 445 2 6 2 88 0 3 3 3 7 3 8 3 4 4 4 4 7 4

Frequency Distributions & Histograms ,[object Object],[object Object]

Frequency Distributions & Histograms ,[object Object],[object Object],[object Object],[object Object]

Frequency Distributions & Histograms ,[object Object]

Frequency Distributions & Histograms ,[object Object],Clearly, the largest group are single member law firms and the frequency decreases as the number of lawyers in the firm increases.

Frequency Distributions & Histograms ,[object Object],The largest group of students bought 5 or 6 textbooks with 3 or 4 being the next largest frequency.

Example of Frequency Distribution ,[object Object],[object Object]

Example of Frequency Distribution ,[object Object]

Histogram for Continuous Data ,[object Object],[object Object]

Histogram for Continuous Data ,[object Object]

Cumulative Relative Frequency Table ,[object Object]

Cumulative Relative Frequency Plot ,[object Object]

Illustrated Distribution Shapes Unimodal Bimodal Multimodal Skew negatively Symmetric Skew positively

Histograms with uneven class widths ,[object Object]

Histograms with uneven class widths ,[object Object],This choice for the density makes the area of the rectangle equal to the relative frequency.

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