**Important Formulas**

1.
The
mean for grouped data can be found by the following methods:

i.

**Direct method:**In direct method, we use the following formula:
ii.

**Assumed mean method:**In assumed mean method, we use the following formula:
iii.

**Step deviation method:**In this method, we use the following formula:
2.
The
mode for grouped data can be found by the following formula:

where

*l =*lower limit of modal class*h*= size of the class interval

*f*= frequency of the modal class

_{1}*f*= frequency of the class preceding the modal class

_{0}*f*= frequency of the class succeeding the modal class

_{2}3. The cumulative frequency of a class is the frequency obtained by adding the frequencies of all the classes preceding the given class.

4.
The
median for grouped data is found by the following formula:

where

*l =*lower limit of median class*n*= number of observations

*cf*= cumulative frequency of class preceding the median class

*f*= frequency of median class

*h*= class size

5.
We
can represent a cumulative frequency distribution graphically as a cumulative
frequency curve, or an ogive of the less than type and of the more than type.

6.
The
median of grouped data can be obtained graphically as the x-coordinate of the
point of intersection of the two ogives, e.g., intersection of less than type
and more than type ogive.