In Statistics Mean, Median and Mode are known as the measures of central tendencies.
The mean of a given data is given by the sum of values of all the given observations divided by the number of observations.
Mean of a given data (
)=
.
There are three methods to find the mean of a grouped data are:
- Direct Method
- Assumed Mean Method
- Step-deviation Method
Direct method:
Mid-point or Class mark (x
i) =
Mean of a given data using direct method (
) =
.
Where f
i is frequency of the given class interval.
Assumed Mean Method:
Mean of grouped data using assumed mean method (
) = A +
Where d
i = x
i - A.
A is an Assumed Mean.
f
i is frequency of the given class interval.
d
i is Deviation of the assumed mean from a class mark.
Step-deviation Method:
Mean of grouped data using step-deviation method (
) = A + h [
]
Where u
i =
A is an Assumed Mean.
f
i is frequency of the given class interval.
h is class size.
- The step deviation method is more suitable, if the deviations of the class marks from the assumed mean are larger.
- In step-deviation method, the mean of grouped data remains the same for any non-zero numbers and , such that ui = .