Question

In Applied Life Data Analysis (Wiley, 1982), Wayne Nelson presents the breakdown time of an insulating fluid between electrodes at 34kV. The times, in minutes, are as follows: 0.20, 0.73, 0.99, 1.29, 2.84, 3.34, 4.07, 4.69, 4.86, 6.53, 7.45, 8.07, 8.21, 12.39, 31.67, 32.53, 33.92, 36.00, and 72.72. Calculate the sample mean and sample deviation of the breakdown data.

Answer 1

xbar=14.3421

s=18.7920

Explanation:

sample mean

xbar = ∑x/n = (0.20 + 0.73 + 0.99 +1.29 + 2.84 + 3.34 + 4.07 + 4.69 + 4.86 + 6.53 + 7.45 + 8.07 + 8.21 + 12.39 + 31.67 + 32.53 + 33.92 + 36.00 +72.72)/19=14.3421

where n stands for the size of the sample

sample deviation

s=
`\sqrt{}`(∑
`(x_i - x bar )^2`/(n-1)) =
`\sqrt{}`(∑
`x_i^2` -
`n*xbar^2`)/(n-1)) =
`\sqrt{}`(0.20^2 + 0.73^2 + 0.99^2 +1.29^2 + 2.84^2 + 3.34^2 + 4.07^2 + 4.69^2 + 4.86^2 + 6.53^2 + 7.45^2 + 8.07^2 + 8.21^2 + 12.39^2 + 31.67 ^2+ 32.53^2 + 33.92^2 + 36.00^2 +72.72^2-19*14.3421^2)/(19-1)) = 18.7920