Difference Between Variance and Standard Deviation

Variance vs Standard Deviation

Variation is the common phenomenon in the study of statistics because had there been no variation in a data, we probably would not need statistics in the first place. Variation is described as variance in statistics which is a measure of the distance of the values from their mean. Variance is little or small if the values are grouped closer to the mean. Standard deviation is another measure to describe the difference between expected results and their actual values. Though both closely related, there are differences between variance and standard deviation that will be discussed in this article.

Raw values are meaningless in any distribution and we cannot deduct any meaningful information from them. It is with the help of standard deviation that we are able to appreciate the significance of a value as it tells us how far we are from the mean value. Variance is similar in concept to standard deviation except that it is a squared value of SD. It makes sense to understand the concepts of variance and standard deviation with the help of an example.

Suppose there is a farmer growing pumpkins. He has ten pumpkins of different weights which are as follows.

2.6, 2.6, 2.8, 3.0, 3.1, 3.2, 3.3, 3.5, 3.6, 3.8. It is easy to calculate the average weight of the pumpkins as it is the sum of all the values divided by 10. In this case it is 3.15 pounds. However, none of the pumpkins weighs this much and they vary in weight ranging from 0.55 pounds lighter to 0.65 pounds heavier than the mean. Now we can write the difference of each value from the mean in the following manner

-0.55, -0.55, -0.35, -0.15, -0.05, 0.15, 0.35, 0.45, 0.65.

What to make out of these differences from the mean. , If we try to find the average difference, we see that we cannot find mean as upon adding, negative values are equal to positive values and the average difference cannot be calculated thus. This is why it was decided to square all the values before adding them up and finding the mean. In this case, squared values come up as follows

0.3025, 0.3025, 0.1225, 0.0225, 0.0025, 0.0025, 0.1225, 0.2025, 0.4225.

Now these values can be added and divided by ten to arrive at a value which is known as variance. This variance is 0.1525 pounds in this example. This value does not hold much significance as we had squared the difference before finding their mean. This is why we need to find the square root of variance to arrive at standard deviation. In this case it is 0.3905 pounds.

In brief:

• Both variance and standard deviation are measures of spread of values in any data.

• Variance is calculated by taking the mean of the squares of individual differences from the mean of the sample

• Standard deviation is the square root of the variance.