Standard deviation (
) is defined as the square root of the arithmetic mean of the square of the deviation of the values taken from mean.
For an individual series
Example:
Marks | Frequency (f) | Mid value (x) | X2 | fx | | | |
0-10 | 5 | 5 | 25 | 25 | 27 | 22 | 484 |
10-20 | 8 | 15 | 225 | 120 | 27 | 12 | 144 |
20-30 | 15 | 25 | 625 | 375 | 27 | 2 | 4 |
30-40 | 16 | 35 | 1225 | 560 | 27 | 8 | 64 |
40-50 | 6 | 45 | 2025 | 270 | 27 | 18 | 324 |
| n = |
| | |
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From actual mean:
Assumed mean method:
Where d=x-A (A is assumed mean)
Method based on actual data
Variance:
It is square of the standard deviation
Standard deviation = 