# Arithmetic Mean definition, formula and applications

## Definiton

The arithmetic mean of a set of data maybe defined as the sum of the values divided by the number of values in the set. Its formula is,

where , A=Arithmetic mean

n= number of observation

i= 1,2,3,4,...,n.

More precisely we can say, The arithmetic mean is an average or central value of  observations obtained by summing the observation and divide them by the number of observations. This is the simplest measure of the measure of central tendency. We conduct arithmetic mean of numerical statistical data which are representative sample of a population.

Merits of arithmetic mean are-

• Arithmetic mean is easy to calculate.
• It is rigidly defined.
• It is based on all observations.
• Observations are not to be arranged in order.
• It provides a sound basis for comparison of two series.
• It can be calculated if partial calculations are available.
• It is less susceptible to sampling fluctuations.
• Arithmetic mean is most suitable for further algebraic treatment.

Detnerits of arithmetic mean are-

• Arithmetic mean is too much affected by extreme values.
• Mostly it does not correspond to any value or the set of observations.
• It cannot be calculated for frequency distribution with open-end classes
• It does not convey any information about the spread or trend of data.
• It is not a suitable measure of central value in case of highly skewed distribution.

For the above demerits , we use geometric mean and harmonic mean instead of arithmetic mean. If the measure of central tendency failed to describe the data then we use measure of dispersion.

### Population mean vs sample mean

The population mean is based on the values of each and every item of the population, whereas the sample mean is based on the values of items selected in the sample from the population. If we have a random sample, then the sample mean is an estimate of the population mean.

### Pooled mean

The pooled mean is the mean of the data that would be obtained by combining two or more sub-group means into a single mean.