Page 119 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Quantitative Techniques – I

Notes
Did u know?
3median = mode + 2 mean
mode = 3median – 2 mean
2mean = 3median – mode.

Self Assessment

Fill in the blanks:
22. .......................is that value of the variate which occurs maximum number of times in a
distribution and around which other items are densely distributed.
23. The concept of mode, as a measure of central tendency, is preferable to mean and median
when it is desired to know the .............................
24. For a moderately skewed distribution, the difference between mean and mode is
approximately ......................... the difference between mean and median

6.6 Geometric Mean

The geometric mean of a series of n positive observations is defined as the nth root of their
product.

6.6.1 Calculation of Geometric Mean

Individual Series

If there are n observations, X , X , ...... X , such that X > 0 for each i, their geometric mean (GM)
1 2 n i
1
1 n n
,
is defined as X X 2 .....................X n X i , where the symbol P is used to denote the
1
n i 1
product of observations.
To evaluate GM, we have to use logarithms. Taking log of both sides we have

1
.
log (GM) = log( X X ....... X )
1
2
n
n
1 log X i
log 1 log 2  log
n
Taking antilog of both sides, we have
log X
i
GM = antilog n .

This result shows that the GM of a set of observations is the antilog of the arithmetic mean of
their logarithms.

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