Standard deviation - comprehensive study approach

Variance is the mean of the squared deviations from the mean.

Instead of finding absolute deviation where we ignored negative signs obtained by subtracting mean from values, we square the difference from the mean. If we had deviation d from the mean, we get another column for d².

Consider the following set of data:

42, 45, 39, 52, 48, 47, 50, 43, 36, 37

The mean for the data is

42 + 45 + 39 + 52 + 48 + 47 + 50 + 44 +

36 + 37 =440

The table below shows deviation from the mean of data representing some marks in a math test.

from the table above, the sum of d² is 268. That is Σd² = 268.00

the variance, sometimes written as σ² is given as Σd² divided by total frequency N. That is;

In the example above:

Standard deviation σ

It is also known as the root mean square deviation and is obtained by getting the square root of the variance. In the example above, The standard deviation, sometimes abbreviated as s.d will be given by:

Standard Deviation For a grouped data

standard deviation is useful for a large data.

consider the table below that contains marks distribution for some 40 students.

We first calculate the mean for the data using the methods of getting mean for the grouped data.

Here i use the assumed mean of 5.5. I choose this value because it has little value of midpoint and frequency, hence not likely to loose a lot of accuracy when it is reduced to zero