To find standard deviation:
1. Calculate the mean by adding up all the data pieces and dividing it by the number of pieces of the data.
2. Subtract mean from every value
3. Square each of the differences
4. Find the average of squared numbers calculated in point number 3 to find the variance.
5. Lastly, find the square root of variance. That is the standard deviation.
For example, Take the values 1,2,3,5 and 8
Step 1: Calculate the mean
1+2+3+5+8 = 19
19/5 = 3.8 (mean)
Step 2: Subtract mean from every value
1- 3.8 = -2.8
2- 3.8 = -1.8
3- 3.8 = -0.8
5- 3.8 = 1.2
8- 3.8 = 4.2
Step 3: Square each difference
-2.8*-2.8 = 7.84
-1.8*-1.8 = 3.24
-0.8*-0.8 = 0.64
1.2*1.2 = 1.44
4.2*4.2 = 17.64
Step 4: Calculate the average of the squared numbers to get the variance
7.84+3.24+0.64+1.44+17.64 = 30.8
30.8/5 = 6.16 (Variance)
Step 5: Find the square root of the variance
The square root of 6.16 = 2.48
Thus, the Standard deviation of values 1,2,3,5 and 8 is 2.48
Graphically, the standard deviation of 2.48 can be represented like below:
Standard Deviation curve
Few real-life implementations of standard deviation include:
1. Grading Tests – If a teacher wants to know whether students are performing at the same level or whether there is a higher standard deviation.
2. To calculate the results of any Survey – If someone wants to have some measure of the reliability of the responses received in the survey, to predict how a bigger group of people may answer the same questions.
3. Weather Forecasting – If a weather forecaster is analyzing the low temperature forecasted for three different cities. A low standard deviation will always show a reliable weather forecast.
