Understanding Standard Deviation

I often hear from friends & colleagues that understanding the concept of Standard Deviation is not very intuitive and not easy to understand.

Well, actually it’s true & you can verify it on Wikipedia 😊 standard deviation. At the same time, it is very critical concept because of its vast use in Statistics, Quantitative Analysis and Data science.

In this post, I have explained the concept of standard deviation in simplest possible way.

• Key properties of a Data Set

For a given set of data, you can find out following properties:

1. Central Tendency of Data. One of the ways to measure central tendency is – Mean (Average).
2. Variability in the Data. In some set of data, data values are concentrated towards the mean and in other data values are more widely spread out from mean. One option to measure of variability is the standard deviation. So standard deviation will tell you how far data values are from the mean.

• How to calculate the Standard Deviation

You can use Excel Formula = STDEV.P() or you can follow this manual procedure:

1. Calculate the deviation of each data value from mean and square them.
2. Take the sum of all deviations and divide by no. of values in the data. We now have calculated variance.
3. Take the square root of variance.

Let’s take an example: You have a Data Set of 10 values containing time in minutes you took to reach Office from Home: [30, 50 , 80 , 25 , 100 , 42 , 28 , 35 , 44 , 56 ]

Mean comes out to be = 49 mins and by following the above procedure, the standard deviation = 23 mins. 

• Interpreting the standard deviation

Let’s pick a value from our Data Set – "25" which means it took you 25 mins to reach Office, you can mention it in this way – my travel time was 24 mins less than my average travel time of 49 mins. Also 23 mins = 1 standard deviation (24/23) , you can say that – my travel time was one standard deviation below my average travel time of 49 mins.

Let’s pick another value – "80" which means it took you 80 mins to reach Office, you can mention it in this way – my travel time was 31 mins more than my average travel time of 49 mins. Since 31 mins = 1.3 standard deviation (31/23), You can say that – my travel time was 1.3 standard deviations more than my average travel time of 49 mins.

You are measuring the variability in the data and also able to express data values in terms of how many standard deviations away they are from Mean.

This is my simple take on Standard Deviation.