Calculate the range variance and standard deviation for the

Calculate the range variance and standard deviation for the following sample. 0.9. 0, 0, -4, 4, -2, 4, 0, -4, 4, -4, 0, -1, -2, -4, 0, 4

Solution

Range is defined as the difference between the maximum value and the minimum value in the sample

Range for the above sample = (Max value) - (Min value) = 4 - (-4) = 8

Hence the range for the sample is equal to 8

For calculating the variance and SD, we need to calculate the mean first

Mean = sum of all numbers/numbers count

=> ( 0.9 + 0 + 0 - 4 + 4 - 2 + 4 + 0 - 4 + 4 - 4 + 0 - 1 - 2 - 4 + 0 + 4)/17

=> -4.1/17 = -0.2411

Variance = 1/(n-1) sigma (x - mean)^2

=> 1/16 [ (-0.2411 - 0.9)^2 + (-0.2411 - 0)^2 + (-0.2411 - 0)^2 + (-0.2411 + 4)^2 + (-0.2411 - 4)^2 + (-0.2411 + 2)^2 + (-0.2411 - 4)^2 + (-0.2411 - 0)^2 + (-0.2411 + 4)^2 + (-0.2411 - 4)^2 + (-0.2411 + 4)^2 + (-0.2411 - 0)^2 + (-0.2411 + 1)^2 + (-0.2411 + 2)^2 + (-0.2411 + 4)^2 + (-0.2411 - 0)^2 + (-0.2411 - 4)^2]

=> 1/16 * 136.82 = 8.55125

Standard Deviation = (Variance)^(0.5) = 2.924