The geometric mean takes a set of positive numbers, multiplies them together, and then takes the root based on how many numbers there are. It proves particularly useful for rates and proportions, as it tends to reveal more about the way the values interrelate than an arithmetic mean would. It has the added advantage of reducing the effect of extremely high or low numbers so that a more accurate average may result in those circumstances.
Definition: The geometric mean is the measure of central tendency which is very helpful in working with sets of positive numbers. It is defined as the n th roots of the product of n values.
The formula for the geometric mean (GM) of a set of positive numbers
Notation In GM Formula:
Question 1: Compute the geometric mean of 4 and 3.
Solution: Applying G.M. formula, the G.M. of 4 and 3 will be:
Geometric Mean will be √(4×3)
= 2√3
So, GM = 3.46
Question 2: Compute the geometric mean of 4, 8, 3, 9 and 17?
Solution:
Step 1: n = 5 is the number of values. Now, calculate 1/n.
1/5 = 0.2.
Step 2: Calculate geometric mean using the following formula:
(4 × 8 × 3 × 9 × 17)0.2
Geometric Mean = 6.814
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The geometric mean takes a set of positive numbers, multiplies them together, and then takes the root based on how many numbers there are. It proves particularly useful for rates and proportions, as it tends to reveal more about the way the values interrelate than an arithmetic mean would. It has the added advantage of reducing the effect of extremely high or low numbers so that a more accurate average may result in those circumstances.
Definition: The geometric mean is the measure of central tendency which is very helpful in working with sets of positive numbers. It is defined as the n th roots of the product of n values.
The formula for the geometric mean (GM) of a set of positive numbers
Notation In GM Formula:
Question 1: Compute the geometric mean of 4 and 3.
Solution: Applying G.M. formula, the G.M. of 4 and 3 will be:
Geometric Mean will be √(4×3)
= 2√3
So, GM = 3.46
Question 2: Compute the geometric mean of 4, 8, 3, 9 and 17?
Solution:
Step 1: n = 5 is the number of values. Now, calculate 1/n.
1/5 = 0.2.
Step 2: Calculate geometric mean using the following formula:
(4 × 8 × 3 × 9 × 17)0.2
Geometric Mean = 6.814
Other Related Sections
NCERT Solutions | Sample Papers | CBSE SYLLABUS| Calculators | Converters | Stories For Kids | Poems for Kids| Learning Concepts | Practice Worksheets | Formulas | Blogs | Parent Resource
Admissions Open for
An integral formula provides a method to evaluate the integral of a function, representing the area under the curve of that function or the accumulation of quantities.
Integral tables offer precomputed antiderivatives for various functions, simplifying the process of finding integrals for complex or unfamiliar functions.
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