Page 120 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Unit 6: Measures of Central Tendency

Notes
Example: Calculate geometric mean of the following data:
1, 7, 29, 92, 115 and 375

Solution:
Calculation of Geometric Mean

X 1 7 29 92 115 375 log X
log X 0.0000 0.8451 1.4624 1.9638 2.0607 2.5740 8.9060

log X
8.9060
= antilog n = antilog 6 = 30.50

GM = antilog = antilog = 30.50

Ungrouped Frequency Distribution

If the data consists of observations X , X , ...... X with respective frequencies f , f , ...... f , where
1 2 n 1 2 n
n
f i N , the geometric mean is given by:
i 1

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

n
1
or GM = antilog N f i log X i , which is again equal to the antilog of the arithmetic mean of
i 1
the logarithm of observations.

Example: Calculate geometric mean of the following distribution:

X : 5 10 15 20 25 30
f : 13 18 50 40 10 6

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