Question

how do i find sample standard deviation from the range frequency table?

Answer 1

The range frequency table consists of classes and class frequency. So to get sample standard deviation first calculate mean. The formula to caculate standard deviation form frequency table is as below

where f is class frequency of each class

m is midpoint of class, n is total frequency and is mean

Here is an solved example of calculating sample standard deviation using range frequency table. There are five classes with following class frequency

Calsses	10-20	20-30	30-40	40-50	50-60
Class frequency	12	9	3	7	5

m is midpoint of each class which is obatined as taking sum of lower and upper class limit and dividing by 2

So the midpoint of first class 10-20 is (10+20)/2 = 30/2 =15

In simialr way we calculate midpoint for each class.

The formula for mean is

So the table for calculation of mean and standard deviation is as follows

The above table gives detai calculation method for sample standard deviation.

Hope you will get from it.