Statistics >> Measures of Central Tendency
So far, we have learned the techniques of data collection and summarising and condensing data into various tables and graphs. Now, we shall deal with some arithmetic procedures that can be used for analyzing and interpreting data.
Measures of central tendency also known as averages describe the tendency of individual items to cluster or concentrate around the centre in a frequency distribution. The most important objective of measures of central tendency is to determine a single representative value for the entire series. They perform the function of giving a concise picture of the entire group and hence they are useful as a basis for comparison with other groups of data.
The following measures of central tendency are commonly used in practice.
(i) Arithmetic Mean (A.M.) or simply mean
(iv) Geometric Mean (G.M.) (v) Harmonic Mean (H.M.)
CHARACTERISTIC OF AN: IDEAL AVERAGE
An average to be considered as an ideal one should posses the following characteristics.
(i) It should be easy to understand and easy to calculate.
(ii) It should be rigidly defined i.e., it should have one and only one interpretation.
(iii) It should be based on all the observations of the series.
(iv) It should be capable of further algebraic treatment i.e., its use in further statistical theory is enhanced.
(v) It should be affected least by fluctuations of sampling.
(vi) It should be affeted least by extreme values i.e., too large or too small values.
Greek alphabet S (capital sigma) is used to denote sum. If a variable x takes the values x1, x2, ............ xn then the sum
x1 + x2 +............ +xn = Σni=1 X i
It implies that minimum value i can take is I and maximum value is n and i takes only integral values.
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