Variance and Standard Deviation

Variance

Variance is a measurement of the spread between numbers in a given data set.

Below is the formula to calculate Variance ,just remember we need to use n-1(where n is count of observations/population/sample) in when we are using sample (click here to know about Sample vs Population).

Standard deviation:

Standard deviation measures the spread of a data distribution. The more spread out a data distribution is, the greater its standard deviation.

Click her to know more about distributions.

standard deviation is equal to the square root of the variance:

Below are the formulas to calculate the Variance and Standard deviation

Where

• X is individual one value
• N is size of population
• x̄ is the mean of population

Lets calculate Variance and Standard Deviation:

 Let’s take the below dataset of ages for students.

Ages = (10,11,12,14,11,16,18,13,15,90)

Calculating Variance:

1. Mean of our dataset = 10+11+12+14+11+16+18+13+15+90/9 = 21
2. Find the distance from Mean to each data point

  ((10-21),(11-21),(12-21),(14-21),(11-21),(16-21),(18-21),(13-21),(90-21),(15-21))  = (-11,-10,-9,-7,-10,-5,-3,-8,69,-6)

3. Square the difference= (121,100,81,49,100,25,9,64,4761,36)
4. Variance = Mean of squared Difference = 121+100+81+49+100+25+9+64+4761+36/10 = 534.6

Calculating the Standard Deviation:

        It is very straightforward Square root of variance is Standard Deviation.

   SD = sqrt(534.6) = 23.12142

Coefficient of variation:

 Some points to remember:

1.    If variance is high, that means you have larger variability in your dataset. In the other way, we can say more values are spread out around your mean value.
2.    Standard deviation represents the average distance of an observation from the mean
3.    The larger the standard deviation, larger the variability of the data.