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    Home > Statistics Tutorial > Arithmetic Mean

ARITHMETIC MEAN

The arithmetic mean is perhaps the most commonly used statistical mean to measure the central tendency of data.

The arithmetic mean is also called the "average". It is used in most scientific experiments.

Mathematically, the arithmetic mean is given by:

arithmetic mean
 =
Sum of all datapoints
Total number of data-points

or more complicated (from wikipedia):

Arithmetic Mean

EXAMPLES

If there are three numbers in a data-set, add them and divide by three:
arithmetic mean
 =
x1 + x2 + x3
3

Or if there are four numbers, add them and divide by 4:

arithmetic mean
 =
x1 + x2 + x3 + x4
4

For example, the time in seconds taken for a particular chemical reaction under the same laboratory conditions might give values of 11.6, 12.1, 11.8, 11.5 and 12.0.

arithmetic mean
 =
Sum of datapoints
Total number of data-points

arithmetic mean
 =
11.6 + 12.1 + 11.8 + 11.5 + 12.0
5

arithmetic mean
 = 11.8

The arithmetic mean of these numbers is 11.8.

This would be the time as measured by the experiment. The differences can be attributed to random errors like random fluctuations in temperature and humidity in the laboratory.

When the word mean is used, it generally refers to the arithmetic mean.
The mean gives very useful information in cases where the data is relatively symmetric. For example, if the data is nearly normally distributed, then the mean is the best measure of central tendency. However, if the data is very skewed, then the arithmetic mean might become misleading.

For example, a commonly quoted number in the placement of business schools is the average salary of the outgoing batch.

IS THE ARITHMENTIC MEAN MISLEADING?

When the arithmetic mean is used to calculate this, it can be misleading because the salaries can be widely spread. Thus it may happen that 10% of the class have gotten excellent job offers while half the class is without jobs. Even in such a scenario, the mean salary can be a good number, but it hides facts behind it. The median becomes a much better measure of the salaries of the students in this case.

However, in some cases, even when the data is skewed, the arithmetic mean gives some valuable information about the data but it needs to be interpreted in the right manner.

The Gross Domestic Product or GDP used in economics to determine the financial well being of a country is an arithmetic mean. The total value of goods and services produced in the country when averaged out over the total population gives a measure of GDP. The GDP tells us nothing about the distribution of wealth inside the country, but can be a good parameter for the country to work with in improving the economic condition of its citizens.


by Siddharth Kalla (2009).



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