Standard deviation is a statistical measure of spread or variability.The standard deviation is the root mean square (RMS) deviation of the values from their arithmetic mean.
The square of the standard deviation. A measure of the degree of spread among a set of values; a measure of the tendency of individual values to vary from the mean value.
Σ = Sum of X = Individual score M = Mean of all scores N = Sample size (Number of scores) Variance : Variance = s2
To find the Standard deviation of 1,2,3,4,5.
| X | M | (X-M) | (X-M)2 |
| 1 | 3 | -2 | 4 |
| 2 | 3 | -1 | 1 |
| 3 | 3 | 0 | 0 |
| 4 | 3 | 1 | 1 |
| 5 | 3 | 2 | 4 |
4+1+0+1+4 = 10
N = 5, the total number of values. Find N-1. 5-1 = 4
√10/√4 = 1.58113
To find the Standard deviation of 1,2,3,4,5.
| X | X2 |
| 1 | 1 |
| 2 | 4 |
| 3 | 9 |
| 4 | 16 |
| 5 | 25 |
s = square root of[(sum of Xsquared -((sum of X)*(sum of X)/N))/(N-1)] = square root of[(55-((15)*(15)/5))/(5-1)] = square root of[(55-(225/5))/4] = square root of[(55-45)/4] = square root of[10/4] = square root of[2.5] s = 1.58113
To find the Population Standard deviation of 1,2,3,4,5. Perform the steps 1 and 2 as seen in above example.
√10/√5 = 1.414
To find the Variance of 1,2,3,4,5. After finding the standard deviation square the values. (1.58113)2 = 2.4999 Same for Population standard deviation. (1.414)2 = 2
This tutorial will help you dynamically to find the standard deviation problems.
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