Please help me understand how to find the standard deviation of grouped data.
We suggest you set out your calculation using a table with headings:
|Class||Midpoint (x)||Frequency (f)||f × x||f × x2|
Notice these are all the headings you need to work out the mean,
plus an extra "fx2" column.
Work out the mean using:
(Click here to see an example of working out the mean of a grouped distribution)
... and the variance using this formula:
Square root the variance to calculate the standard deviation.
Here is a worked example:
100 parcels were weighed. Their masses were as follows:
Estimate the mean and standard deviation of the masses.
Draw a table like this:
|Mass, g||Midpoint (x)||Frequency (f)||f × x||f × x2|
The estimate of the mean is:
mean = 71000 ÷ 100 = 710 grams.
The estimate of the variance is:
var = 61093750 ÷ 100 - (710)2 = 106837.5
...and the standard deviation is the square root of the variance:
standard deviation = sqrt(106837.5) = 326.86 grams (2dp)