Presenting Data in Tables and Charts for

Categorical and Numerical Data

Tabulating and GraphingUnivariate Categorical Data

Categorical Data

Tabulating DataThe Summary Table

Graphing Data

Pie Charts

Pareto DiagramBar Charts

Tabulating and Graphing UnivariateCategorical Data

The Summary TableA summary table for categorical data is similiar in format to the frequency distribution table for numerical. It has class groupings (i.e., categories), frequency and percentage frequency.

The Bar ChartIn a bar chart, each category is depicted by a bar, the length of which represents the frequency or percentage of observations falling into a category.The Pie ChartThe pie chart is based on the fact that the circle has 360o. The pie is divided into slices according to the percentage in each category.

Tabulating and Graphing UnivariateCategorical Data

The Pareto DiagramThe pareto diagram is a special type of vertical bar chart in which the categorized responses are plotted in the descending rank order of their frequencies and combined with a cumulative polygon on the same graph.

Tabulating and Graphing UnivariateCategorical Data

Tabulating and Graphing BivariateCategorical Data

The Contigency Table The contigency table display two categorical variables, a two way table of cross-classification.The Side by-Side Bar ChartA useful way to visually display bivariate categorical data when looking for pattern or relationships is by constructing a side-by-side bar chart.

Among the methods for describing and communicating statistical information, well-designed graphical displays are usually the simplest and the most powerful. Good graphical displays reveal what the data are conveying.

Graphical Excellence and Common Errors in Presenting Data

The basic features of a proper graph include the following:

1. Showing the data2. Getting the viewer to focus on the substance of

the graph, rather than on how the graph was developed

3. Avoiding distortion4. Encouraging comparasions of data5. Serving a clear purpose6. Being integrated with the statistical and verbal

descriptions of the graph

Graphical Excellence and Common Errors in Presenting Data

Principles of Graphical Excellence:1. Graphical excellence is a well-designed presentation of

data that provides subtance, statistic, and design.2. Graphical excellence communicates complex ideas

with clarity, precision, and efficiency.3. Graphical excellence gives the viewer the largest

number of ideas in the shortest time, with the least ink.4. Graphical excellence almost always involves several

dimensions.5. Graphical excellence requires telling the truth about the

data.

Graphical Excellence and Common Errors in Presenting Data

A frequency distribution is a summary table in which the data are arranged into conveniently established, numerically ordered class grouping or categories.In constructing the frequency distribution, attention must be given to selecting the appropriate number of class groupings for the table, obtaining a suitable class interval, or width of each grouping, and establishing the boundaries of each class grouping to avoid overlapping.

Constructing a Frequency Distribution Table

Selecting the Number of ClassesIn general, however, the frequency distribution should have at least five class groupings, but no more than 15. If there are not enough class groupings or if there are too many, little new information is leaned.

Constructing a Frequency Distribution Table

Constructing a Frequency Distribution Table

Obtaining the Class Intervals

Establishing the Boundaries of the ClassesTo construct the frequency distribution table, clearly defined class boundaries for each class grouping should be established so that the observations can be properly tallied into the classes.The class-midpoint is the point halfway between the boundaries of each class and is representative of the data within that class.

groupingsclassdesiredofNumberRangeervalofWidth

int =

Relative Frequency and Cummulative Frequency

A relative frequency distribution is obtained by dividing each frequency by the number of observations and multiplying the resulting proportion by 100%A cummulative frequency distribution contains the total number of observations whose values are less than the upper limit for each interval.

Histogram, Polygon and Ogive

A histogram is a chart in which the rectangular bars are contructed at the boundaries of each class.

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Histogram, Polygon and Ogive

The percentage polygon is formed by having the midpoint of each class represent the data in that class and then connecting the sequence of midpoints at their respective class percentages.

Histogram, Polygon and Ogive

The cumulative polygon (ogive) is a graphic representation of a cumulative percentage distribution.

Ogive

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Numerical Data

Ordered Array

Stem and LeafDisplay

Frequency DistributionsCumulative Distributions

Histograms

Polygons

Ogive

Tables

Tabulating Numerical Data: Frequency Distributions

Sort raw data in ascending order:12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58

Find range: 58 - 12 = 46

Select number of classes: 5 (usually between 5 and 15)

Compute class interval (width): 10 (46/5 then round up)

Determine class boundaries (limits): 10, 20, 30, 40, 50, 60

Compute class midpoints: 15, 25, 35, 45, 55

Count observations & assign to classes

Frequency Distributions, Relative Frequency Distributions and Percentage Distributions

Class Frequency

10 but under 20 3 .15 1520 but under 30 6 .30 3030 but under 40 5 .25 25 40 but under 50 4 .20 2050 but under 60 2 .10 10 Total 20 1 100

RelativeFrequency

Percentage

Data in ordered array:12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58

Graphing Numerical Data: The Histogram

Histogram

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001234567

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12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58

No Gaps Between

Bars

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Graphing Numerical Data: The Frequency Polygon

Fre q u e n c y

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Class Midpoints

Data in ordered array:12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58

Tabulating Numerical Data: Cumulative Frequency

Cumulative CumulativeClass Frequency % Frequency10 but under 20 3 1520 but under 30 9 4530 but under 40 14 70 40 but under 50 18 9050 but under 60 20 100

Data in ordered array:12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58

Graphing Numerical Data: The Ogive (Cumulative % Polygon)

Ogive

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Class Boundaries (Not Midpoints)

Data in ordered array:12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58