Question

Complete the variance and standard deviation of the following observations of marks of 5 students of a tutorial group: Marks out of 25:8,12,13,15,22

Answer 1

Here, Mean `(barX) = (8+12+13+15+22)/5 = 70/5 = 14`
`:. x_i-barX = -6,-2,-1,1,8`
`=> (x_i-barX)^2 = 36,4,1,1,64`
`:. sum (x_i-barX)^2 = 106`
Now, Variance `(sigma^2) =1/nsum (x_i-barX)^2 = 106/5 = 21.2`
Standard deviation `(sigma) = sqrt(21.2) = 4.6`