# Geometric Mean
Geometric mean is defined as the nth root of the product of N items or values. It there are two items. We take the square root; if there are three items, cube root; and so on. When the number of items is three or more the task of multiplying the number and of extracting the root becomes excessively difficult.
## Merits and Limitations of Geometric Mean
### Merits:
1. It is based on each and every item of series.
2. It is rigidly defined.
3. It is useful in averaging ratios and percentages and in determining rates of increase and decrease.
4. It gives less weight to large items and more to small ones than does the arithmetic average. It is because of this reason that geometric mean is never larger than the arithmetic mean, on occasions it may turn out to be same as the arithmetic mean, but usually it is smaller.
5. It is capable of algebraic manipulations.
### Limitations:
1. It is difficult to understand.
2. It is difficult to compute and to interpret and so has restricted application.
3. It cannot be computed when there are both negative and positive values in a series or one or more of the values are zero.
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