Q.3 What is Geometric Man? Give Algebraic Characteristics of Geometric Mean and state when Geometric Mean is useful.
4 years ago
Business Statistics
Geometric mean is the nth root of the product of N items or values.
Calculation of Geometric Mean (G) :
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Individual Series |
Discrete & Continuous Series |
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G = Antilog ∑ log X N |
G = Antilog ∑f log X N |
Algebraic Characteristics of Geometric Mean :
- The product of the items remain unchanged if each item is replaced by geometric
- Geometric mean cannot be found if the value of some item in the series is negative or
- The product of corresponding ratios on either side of the geometric mean is always
- Not affected by changing the sequence of Geometric mean is appropriate or useful :-
- When ratios or percentages are to be
- In determining rates of increase or
- When the different values are at vast
- Q.3 What is Harmonic Mean? In which circumstances Harmonic Mean is used.
Ans.: Harmonic mean of a series is the reciprocal of the arithmetic mean of the reciprocal of the values of its items.
Calculation of Harmonic Mean (H.M.) :
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Individual Series |
Discrete & Continuous Series |
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H.M. = Reciprocal ∑ Reci.X N |
H.M. = Reciprocal ∑ (Reci.X .f) N |
Harmonic Mean is used in the following cases : -
- For determining average speed or velocity
- To find out average price
If the item given in the question which is variable is to be kept as constant in the answer, or vice versa, then harmonic mean will be calculated.
Surya Bikram Bhandari
Nov 14, 2021