Question

Describe what a standard deviation is conceptually.

Answer 1

Answer)

Standard deviation tells us about the distance between data values from mean

Or standard deviation is the average distance of data values from the mean

If we have the following data

8, 8, 8, 8

Standard deviation for this data is 0

As there is no difference in between mean and data values

But if we have data

1, 2, 3, 4

Then we need to follow the below mentioned steps to calculate s.d

Mean = sum of the observations/number of observations

Mean = (1+2+3+4)/4 = 2.5

Then we need to first subtract mean from each and every observation and then we need to take.the square and finally add the results

= (1-2.5)^2 + (2-2.5)^2..

= 5

Now we need to divide by n and take the square root

S.d = √5/4 = 1.12