How do you find the geometric mean and harmonic mean
Finding geometric mean and harmonic mean :
In Mathematics, geometric mean and harmonic mean are the two different types of mean to calculate the average of the given values. The procedure to calculate the geometric and harmonic mean are given below:
Step 1:Steps to calculate the geometric mean:
1. Multiply the given numbers together.
2. Take root for the result obtained from step 1, if values are given.
If two values are given, take square root for the result obtained from step 1, or take cube root, if three values are given.
Geometric mean (GM)
Where,
are the given values.
For example, are the two given values, the geometric mean is calculated as follows:
1. Multiply we get
2. Take the square root of , because the number of values given is
Now,
Hence, the geometric mean for is
Step 2: Steps to calculate the harmonic mean:
1. Write down the reciprocal of each given value.
2. Now, calculate the average value of the reciprocal obtained from step 1.
3. Finally, take the reciprocal of the average value.
The formula to calculate the harmonic mean is:
Harmonic mean (HM)
Where,
are the given data values
is the number of values.
Now, consider the same example. and are the two values, then the harmonic mean is calculated as follows:
Step 1: The reciprocal of are, respectively.
Step 2: The average value of is:
Average
Step 3: Now, take the reciprocal of the average value obtained in step 2.
Harmonic mean
Hence, in this way we can find the geometric mean and harmonic mean.