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Arithmetic Mean or Mean is defined as the sum of all the observations divided by the total number of observations. It is usually denoted by \(\overline X\).
Therefore, mean \(\overline X = \frac{\text{Sum of all the observations}}{\text{Total number of observations}}\)
Arithmetic mean or mean is the commonly used method to find the average of the given data.
Methods of finding mean
- If the given collection of data is ungrouped, then the mean is obtained by direct method.
Mean \(\overline X\)
If the number of observations is very long, it is a bit difficult to write them. Hence, we use the Sigma notation \(\sum\) for summation.
That is, , where \(n\) is the total number of observations.
- If the given collection of data is grouped, then the mean is obtained by the following methods.
1. Direct Method:
The formula for finding the arithmetic mean using the direct method is given by:
Click here! To recall the direct method to find mean.
2. Assumed Mean Method:
The formula for finding the arithmetic mean using the assumed mean method is given by:
where \(d_{i} = x_{i} - A\).
Click here! To recall the assumed mean method to find mean.
3. Step Deviation Method:
The formula for finding the arithmetic mean using the step deviation mean method is given by:
where \(d_{i} = \frac{ x_{i} - A}{c}\).
Click here! To recall the step deviation method to find mean.
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