DATA FROM A SAMPLE OF 25 STUDENTS

A B B AB 0

0 0 B AB B

B B 0 A 0

A 0 0 0 AB

AB A 0 B A

12 14 19 18

15 15 18 17

20 27 22 23

22 21 33 28

14 18 16 13

112 100 127 120 134 118 105 110 109 112

110 118 117 116 118 122 114 114 105 109

107 112 114 115 118 117 118 122 106 110

116 108 110 121 113 120 119 111 104 111

120 113 120 117 105 110 118 112 114 114

DATA ON HIGH TEMPERATURES IN OF

Source: The World Almanac and Book of Facts

DATA ON TESTING CENTER THE NUMBER OF CARDIOGRAM PERFORMED EACH DAY FOR 20 DAYS

25 31 20 32 13

14 43 2 57 23

36 32 33 32 44

32 52 44 51 45

Dot Plot is a graphical summaries of data. A horizontal axis shows the range of values for

the observations. Each data value is represented by a dot placed above the axis.

Dot Plots show the details of the data and are useful for comparing the distribution of data

for 2 or more variables.

DOT DIAGRAM (DOT PLOT)

The data shown below are the number of case files for 30 “law and consulting firms” in Ankara in 2010.

83 83 75 80 76 80 81 84 79 80 84 86 72 82 82 79 81 79 80 73

90 82 81 75 77 80 79 76 85 85

Construct a dot plot of the given above data.

THE STEM_AND_LEAF DISPLAY

This technique can be used to show both the rank order and a shape of a data set

simultaneously.

To develop a stem_and_leaf display, we first arrange the leading digits of each data value

to the left of the vertical line. To the right of the vertical line, we record the last digit for

each data value as we pass through the observations in the order they were recorded.

The numbers to the left of the vertical line form the STEM.

Each digit to the right of the vertical line is a LEAF

Advantages:

1- It is easier to construct by hand

2- Since it shows the actual data, this display provides more information than histograms

FREQUENCY DISTRIBUTION FOR QUALITATIVE DATA

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InsuranceCriminalDivorceCriminalDivorceCriminalInsuranceCommercialCriminalCriminalCriminalCommercialCriminalInsuranceCyberCommercialDivorce

CommercialCriminalCriminalCriminalCommercialCyberCriminalDivorceCommercialCommercialCommercialCommercialCriminalCyberCommercialInsurance

DATA FROM A SAMPLE OF 50 CASES IN A LAW FIRM

BAR GRAPHS

A Bar graph (chart) is a graphical device for depicting qualitative data summarized in:-Frequency-Relative Frequency-Percent Frequency

On one axis of the graph (usually the horizontal axis) we specify the labels that are used for the classes (Categories) of data.A frequency; relative frequency or percent frequency scale can be used for the other axis of the graph (usually the vertical axis)

FREQUENCY DISTRIBUTION FOR QUANTITATIVE DATA

With quantitative data, we must be more careful in defining the non-overlapping classes to be used in the freq. distribution. There are three steps necessary to define classes for a freq. diApp. with quantitative data.1- Determine the number of non-overlapping classes.2- Determine the width of each class.3- Determine the class limits

1- NUMBER OF CLASSES:Classes are formed by specifying ranges that will be used to group the data. As a general guideline, we recommend using between 5 and 20 classes. For a small number of data items, as few as five or six classes may be used to summarize the data.

Sample Size Number of Classes

Fewer than 50 5 – 6 Classes

50 to 100 7 – 8 Classes

Over 100 9 – 10 Classes

3- CLASS LIMITS:Class limits must be chosen so that each item belongs to one and only one class.

The lower class limit identifies the smallest possible data value assigned to the class.

The upper class limit identifies the largest possible data value assigned to the class.

CLASS MIDPOINT (M): The class midpoint is the value halfway between the lower and upper class limits. The definitions of the Relative Freq. and Percent Freq. Distributions are as the same as for qualitative data

Cumulative Distributions:

Cumulative Distribution is another tabular summary of data (quantitative). Cumulative

Distribution use the number of classes, class widths and class limits developed for the

frequency distributions.

Cumulative Distribution shows the number of data items with values “less than or equal to

the upper class limit” of each class.

We also note that a cumulative relative frequency distribution shows the proportion of data

items, and a cumulative percent frequency distribution shows the percentage of data

items with values less than or equal to the upper limit of each class.

Administrators of a company are considering the possibility of changing the pattern of work hours from 8-hours-day, 5-day week to a 10-hours day, 4-day week. They feel that this change might cut down on absenteeism. In order to help make this decision, the following data were collected on the number of workers absent per day over a 6-week experimental period.

Construct a frequency distribution table for these data

15 9 15 5 16 16 30 7 12 9

23 15 21 16 17 13 20 18 2 31

11 12 27 22 15 14 10 6 19 14

HISTOGRAM

A common graphical presentation for quantitative data is a Histogram. This graphical

summary can be prepared for data previously summarized in either a frequency, relative

frequency or percent frequency distributions.

Variable of interest is placed on the horizontal axis.

The frequency/relative/percent frequency is placed on the vertical axis for each class

which is shown by drawing a rectangle whose base is determined by the class limits on

the horizontal axis and whose height is the corresponding frequency/relative/percent

frequency.

PIE CHART

The pie chart provides another graphical device for presenting frequency and percent frequency distribution for qualitative data.To construct a pie chart:We first draw a circle to represent all of the data. Then we use the relative frequencies to subdivide the circle into sectors, or parts that correspond to the relative frequency for each class.