Standard Deviation for continuous series

In this series too deviations may be taken either from the actual mean or from standard mean. The calculations will be simplified if the deviation are taken from assumed mean.

Step 1:

Take the midpoint of different classes.

Step 2:

Subtract assumed mean from each midpoint to obtain (m-a).

Step 3:

If the width of the class interval is same, then divide each (m-a) by c,

Step 4:

Multiply each frequency with corresponding deviation i.e., fd and obtain Sfd.

Step 5:

Step 6:

Apply the formula

Example:

Calculate the variance and standard deviation from the following data.

Suggested answer: