Standard deviation measures how dispersed the data points are from the mean.
Let’s say you collect the weights of 250 random people on a train, including toddlers and the elderly.
Now, you add all these weights to get the sum.
Then you divide the sum by 250 to get the average weight of these people (this average is also known as the mean).
Let’s say the average comes down to 60 kgs.
Since these are random people, there will be people who weigh 100 kgs and toddlers who weigh about 10 kgs.
In this case, we can say that the data is widely dispersed from the mean.
This means the data is spread quite far (from 10 kgs to 100kgs) from the mean of 60 kgs.
Now, let us consider the weights of 250 international soccer players.
And calculate the mean weight — assume that the average comes to 60 kgs in this case too.
Since most of them will have comparable weightsIt is unlikely that any player would weigh 10 kgs or 100kgs, the individual weights are likely to be quite close to the mean.
From these examples, we can conclude that the standard deviation for the soccer players would be far less than that of the train passengers.
If the actual standard deviation for soccer players comes to be 10 kgs, it means a very high proportion of the players weigh between 50 kgs (60 – 10) and 70 (60 + 10) kgs.
