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Graphic and Tabular Presentation of Data

TABULAR PRESENTATION OF DATA

Raw Data

Ungrouped DataGrouped Data
AgesAges f or Agesf
2518 218-19 5
4519 320-21 23
2220 1122-23 22
2321 1224-25 6
4622 1526-27 4
8423 728-29 etc.
1224 430-31
225 232-33
3426 334-35
1527 1etc.

* note the difference is width of category; 1 versus 2 years

  1. How to group data: some guidelines

Agesf
18-3172
32-4545

  1. 2. Almost every measurement is rounded off, such as height ("5 foot 9 inches" instead of "5 foot 8.89 inches"). One major exception to this is age. Age is looked at two ways:

Age to last Birthday Age to nearest Birthday
Age limits True limits midpoint Age limits true limitsmidpoint
18-1918.00-19.999 19.0018-19 17.50-19.499918.5
20-2120.00-21.999 21.0020-21 19.50-21.499920.5 etc.

m (for continuous variables) =

m (for discrete variables) =

*midpoint: abbreviated : "m"

*discrete variable: the variable's unit of measure cannot be divided infinitely

*continuous variable: the variable's unit of measure that can be divided infinitely.

GRAPHING DATA

  1. Histogram -- for interval data



B. Bar graph -- for nominal data (or ordinal)


SOURCE: GSS91 SURVEY SUBSAMPLE


C. Pie Chart -- for nominal data (or ordinal)

SOURCE: GSS91 SURVEY SUBSAMPLE


*Double hatch marks indicate interruption in the consistently equal intervals. In this case the earliest age in the sample was 15. The double hatch marks indicates that the range 0-9.99 was skipped in the polygon.

D. Frequency polygon -- for interval data

TYPES OF DISTRIBUTION

A. unimodal = one peak (mode)

B. bimodal = 2 modes

C. Skewed distributions are unimodal distributions which are not symmetrical. A positively skewed distribution will have a mean that is greater in value than its median. Its tail will fall on the side of the larger values. A negatively skewed distribution will have a median that is greater in value than it's mean. Its tail will fall on the side of the smaller values. A normal curve skew measures 0, while a positive skew measure is a positive value and the negative skew measure is a negative value.

D. Degree of kurtosis -- more dense or peaked distributions than the Bell curve are called leptokurtic. Flatter distributions than the Bell curve are called platykurtic. A normal kurtosis measures 0. A positive value of kurtosis describes a leptokurtic distribution, while a negative value of kurtosis describes a platykurtic distribution.

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