Geometric Mean
The geometric mean is another measure of central tendency based on mathematical footing, like arithmetic mean. The geometric mean can be defined as:
“The geometric mean is the nth positive root of the product of 'n' positive given values.”
Hence, the geometric mean for a value containing
values such as
is denoted by
of
and given as:
If we have a series of positive values with repeated values such as
which are repeated
times respectively, then the geometric mean will become:
Where
Example:
Find the geometric mean of the values 10, 5, 15, 8, 12.
Solution:
Here,
and
Example:
Find the geometric mean of the following data:
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Solution:
We may write it as below:
Here ,
,
,
,
,
Using the formula of geometric mean for grouped data, the geometric mean in this case will become:
The method explained above to calculate the geometric mean is useful when the values in the given data are small in number and an electronic calculator is available. When a set of data contains a large number of values then we need an alternate way to compute the geometric mean. The modified or alternative way of computing the geometric mean is given as:
For Ungrouped Data
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For Grouped Data
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Example:
Find the geometric mean of the values 10, 5, 15, 8, 12
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Total
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Example:
Find the geometric mean for the following distribution of students’ marks:
Marks
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No. of Students
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Solution:
Marks
|
No. of Students
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Mid Points
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Total
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