Glossary term
Arithmetic Mean: Meaning and Definition
Reviewed and approved by Dr. Anamika ShrivastavaPublished Last updated
The arithmetic mean is the sum of all observations divided by the number of observations. It is the most common average and uses every value, but it is pulled by extreme values. The sum of deviations of the items from the mean is always zero.
In more detail
The mean balances the data: deviations above it exactly cancel those below. It uses every value, which makes it efficient but sensitive to extreme values. Weighted means give more importance to some items, as in price indices. For grouped data it is found from class marks and frequencies.
Example
The values 42, 55, 48, 60, 51, 47, 57 and 40 add up to 400. Dividing by 8 gives a mean of 50.
Key points
- Mean = ΣX ÷ N.
- For grouped data use class marks: Σfm ÷ Σf.
- Affected by extreme values.
Common mistake
Using the mean for skewed data such as incomes. The median is more typical there.
Related terms
Where it is explained
This term is explained in Class 11 Statistics Chapter 5: Measures of Central Tendency.