Question

Find the range and population varriance of the following data set ( 11, 12, 55, 4, 17, 14, 18) (Show your formula)

Answer 1

The formula of range of a dataset is Maximum observation - minimum observation. Here the maximum observation is 55, minimum observation is 4. So the range is 55-4 =51 (ans)

Formula of population variance is:-

Sum ((xi - x_bar)^2) / n), where xi is the ith observation of the dataset of the observation, x_bar is the mean of the population, n is the number of observations.

The formula of mean is the sum of all observations divided by number of observations, which is: (11 +12 +55 +4 +17 +14 +18)/7 = 131/7 =18.71 (upto 2 decimals)

So the population variance will be:

((11 - 18.71)^2 + (12 - 18.71)^2 + (55 - 18.71)^2 + (4 - 18.71)^2 + (17 -18.71)^2+ (14 - 18.71)^2 + (18 -18.71)^2) / 7

= (59.44 + 45.02 + 1316.96 + 216.38 + 2.92 + 22.18 +0.50)/7

= 237. 63 (ans)