Module On Measures Of Central Tendency

Module on Measures of
Central Tendency

Measures of Central
Tendency
There are many ways of describing of a given set of data. A good number of descriptive measures exist in statistics whose use depends largely on the nature of data and the intended purpose of the description. This measure is the measures of position or central tendency, it is use to see how a large set of raw materials can be summarized so that the meaningful essential can be extracted from it.
The most commonly measures of central tendency are the mean, median, and mode.

Properties of the Arithmetic Mean
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easy to compute easy to understand valuable in statistical tool strongly influence by extreme values, this is particularly true when the number of cases is small cannot be compute when distribution contains open-ended intervals

Uses of Mean
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for interval and ratio measurement when greatest sampling stability is desired when the distribution is symmetrical about the center when we want to know the “center of gravity” of a sample

The Arithmetic Mean (X)
The most popular and useful measure of central tendency is the arithmetic mean, which simply refer to as the mean. Widely referred to in everyday usage as the average. The mean of a set of measurement is defined as, sum of measurements mean = -----------------------------------number of measurements
In formula form,
 Xi
X = --------N
Where:

N = total number of measurements
X = represent the mean
Xi = represents the individual scores

The symbol  is a Greek letter sigma, which means sum of. In plain language, the arithmetic is obtained merely by adding the individual scores and dividing the sum by the number of scores.

Mean (ungrouped data)
 Xi

X1 + X2 + X3 + X4 +

X5 + … + Xn

X = ---------------=
-----------------------------------------------------N

N

Raw data: 15
Xi
X = ------------------- =
N

16

19

20

18

15 + 16 + 19 + 20 + 18
--------------------------------------------------------------5

= 17.6

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