Geometric Mean as Central Tendency

In this class, We discuss Geometric Mean as Central Tendency.

The reader should have prior knowledge of mean, median, and mode. Click Here.

The reader will understand how to calculate geometric mean and the situations geometric mean is useful.

Geometric Mean:

nth root of product of all the n data values is called geometric mean.

n is number of data values.

Example:

n = 4

1, 5, 3, 7

GM = ∜1*5*3*7

GM = ∜105

GM = 3.2

We should not use negative and zero value in geometric mean.

Geometric mean works good if there is multiplicative or exponential relation among data.

Arithmetic mean does not work for multiplicative and exponential relation data.

We consider the same example to show how geometric mean is good for multiplicative data.

Example:

1, 3, 9, 27, 81, 243, 729

GM = 7√1 * 3 * 9 * 27 * 81 * 243 * 729

GM = 7√10460353203

Geometric mean used when we using percentages

Example:

Given profits of a company for last three years

1st year profit 12% = 0.12

2nd year loss 8% = -0.08

3rd year profit 2% = 0.02

2nd year we have loss. we write it as – 0.08.

What is the average profit?

To avoid negative values geometric mean equation is changed a little.

GM = 3√((1 + x1) (1+x2)(1 + x3)) -1

Each data value is added with one.

GM = 3√((1.12)(0.98)(1.02)) – 1

GM = 1.67

Geometric mean works when calculating compound interest.

Example:

Principal amount = 10000

The amount we deposited is considered principal amount.

we give compound interest of 0.1 for 25 years.

The below table shows how compound interest is added.

First year 1000 interest is added to principal amount.

second year the interest is added to principal amount.

The second year interest is given for the principal amount 11000.

again the interest is added to principal amount. and interest is given for new principal amount.

This repeats for 25 years.