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Class 10 > Learn Mathematics > What is the difference between Geometric mean and Harmonic...
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What is the difference between Geometric mean and Harmonic mean?

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Although the concept of an average seems simple, we continue to see many people using an incorrect method to calculate averages. We would be surprised if most people were familiar with the three different types of averages mentioned in the title. In fact, many people (including journalists) routinely...
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Although the concept of an average seems simple, we continue to see many people using an incorrect method to calculate averages. We would be surprised if most people were familiar with the three different types of averages mentioned in the title. In fact, many people (including journalists) routinely use the wrong type of average–leading to incorrect results and often poor decisions. read less
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GM=SQURT(a*b) HM=2ab/a+b reciprocal of AM is HM in AM a,a+d,a+2d series in GM-- a, ar, ar^2 .. like that okay.
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Geometric mean (GM) is should be used when discussing average investment returns or interest rates.GM is for the situations when we want the average in multiplicative situation. Harmonic Mean (HM) is a better average when numbers are defined in relations to some unit. HM is best used in situations...
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Geometric mean (GM) is should be used when discussing average investment returns or interest rates.GM is for the situations when we want the average in multiplicative situation. Harmonic Mean (HM) is a better average when numbers are defined in relations to some unit. HM is best used in situations where extreme out liers exist in the population. example-averaging speed. read less
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In mathematics, the geometric mean is a type of mean or average, which indicates the central tendency or typical value of a set of numbers by using the product of their values.The geometric mean is defined as the nth root of the product of n numbers, i.e., for a set of numbers x1, x2, ..., xn, the geometric...
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In mathematics, the geometric mean is a type of mean or average, which indicates the central tendency or typical value of a set of numbers by using the product of their values.The geometric mean is defined as the nth root of the product of n numbers, i.e., for a set of numbers x1, x2, ..., xn, the geometric mean is defined as (X1*X2*X3*X4....Xn)^(1/n). Whereas, Harmonic Mean is the reciprocal of the arithmetic mean of the reciprocals. In other words, it is the number of observations, divided by the sum of reciprocals of the observations. The harmonic mean H of the positive real numbers x1, x2, x3, ...xn > 0 can be derived from the formula:- H= n/(1/X1 + 1/X2 + 1/X3....+1/Xn). read less
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Geometric progression (also known as geometric sequence) is a sequence of numbers where the ratio of any two adjacent terms is constant. The constant ratio is called the common ratio, r of geometric progression. Each term therefore in geometric progression is found by multiplying the previous one by...
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Geometric progression (also known as geometric sequence) is a sequence of numbers where the ratio of any two adjacent terms is constant. The constant ratio is called the common ratio, r of geometric progression. Each term therefore in geometric progression is found by multiplying the previous one by r. Examples of GP:- 3, 6, 12, 24, … is a geometric progression with r = 2 10, -5, 2.5, -1.25, … is a geometric progression with r = -1/2. Harmonic progression is a sequence of numbers in which the reciprocals of the elements are in arithmetic progression. Example of harmonic progression is: 1/3, 1/6, 1/9, ... If you take the reciprocal of each term from the above HP, the sequence will become 3, 6, 9, ..., which is an AP with a common difference of 3. read less
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The GM is for situations we want the average used in a multiplicative situation, such as the "average" dimension of a box that would have the same volume as length x width x height. For example, suppose a box has dimensions 50 x 80 x 100 cm.         ? A cubic box with sides of the GM=73.7 cm would...
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The GM is for situations we want the average used in a multiplicative situation, such as the "average" dimension of a box that would have the same volume as length x width x height. For example, suppose a box has dimensions 50 x 80 x 100 cm.         ? A cubic box with sides of the GM=73.7 cm would enclose the same 400,000 cm3 or 0.4 m3  volume. The harmonic mean is a better "average" when the numbers are defined in relation to some unit.  The common example is averaging speed. For example, suppose that you have four 10 km segments to your automobile trip.  You drive your car: 100 km/hr for the first 10 km110 km/hr for the second 10 km90 km/hr for the third 10 km120 km/hr for the fourth 10 km. read less
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Use the geometric mean when your sample contains fractions. Use the harmonic mean when your sample contains fractions and/or extreme values (either too big or too small). It is more stable regarding out liers. For example:- the arithmetic mean of (1,2,3,4,5,100) is 19.2 whereas the harmonic one is 2....
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The Geometric Mean is a special type of average where we multiply the numbers together and then take a square root (for two numbers), cube root (for three numbers) etc Harmonic Mean. A kind of average. To find the harmonic mean of a set of n numbers, add the reciprocals of the numbers in the set, divide...
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The Geometric Mean is a special type of average where we multiply the numbers together and then take a square root (for two numbers), cube root (for three numbers) etc Harmonic Mean. A kind of average. To find the harmonic mean of a set of n numbers, add the reciprocals of the numbers in the set, divide the sum by n, then take the reciprocal of the result. read less
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If a,b & c are in GP then the Geometric Mean b2=ac. If a,b & c are in HP then the Harmonic Mean 2/b=(a+c)/ac.
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Geometric mean of two number a & b is said to be c if C^2=axb and Harmonic mean of two number a & b is said to be c if C=(2*a*b/a+b).
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