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Unformatted text preview: e a tendency to come to a
central position or an average value. For instance, in a mark distribution,
the individual students may score marks between zero and hundred. In this
distribution, many students may score marks, which are near to the average
marks, i.e. 50. Such a tendency of the data to concentrate to the central
position of the distribution is called central tendency. Central tendency of
the data is measured by statistical averages. Averages are classified into
two groups.
1. Mathematical averages
2. Positional averages
Statistical Averages
Mathematical averages Positional averages Arithmetic mean Median Geometric mean Mode Harmonic mean
Sikkim Manipal University Page No. 169 Research Methodology Unit 11 Arithmetic mean, geometric mean and harmonic mean are mathematical
averages. Median and mode are positional averages. These statistical
measures try to understand how individual values in a distribution
concentrate to a central value like average. If the values of distribution
approximately come near to the average value, we conclude that the
distribution has central tendency.
Arithmetic Mean
Arithmetic mean is the most commonly used statistical average. It is the
value obtained by dividing the sum of the item by the number of items in a
series. Symbolically we say
Arithmetic mean = X/n
Where X
N = the sum of the item
= the number of items in the series. If x1 x2 x3… xn are the values of a series, then arithmetic mean of the series
obtained by
(x1 + x2 + x3… +xn) / n. If put (x1 + x2 + x3… +xn) = X, then arithmetic mean = X/n
When frequencies are also given with the values, to calculate arithmetic
mean, the values are first multiplied with the corresponding frequency. Then
their sum is divided by the number of frequency. Thus in a discrete series,
arithmetic mean is calculated by the following formula.
Arithmetic mean =
Where, fx fx/ f = sum the values multiplied by the corresponding
frequency. f = sum of the frequency If x1 x2 x3… xn are the values of a series, and f1 f2 f3… fn are...
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This note was uploaded on 04/15/2010 for the course MBA mba taught by Professor Smu during the Spring '10 term at Manipal University.
 Spring '10
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