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: 0.15, 0.75, 0.96, 1.35, 2.87, 3.19, 4.01, 4.62, 4.88, 6.43, 7.41, 8.04, 8.24, 12.86, 31.63, 32.61, 33.98, 36.18, and 72.83. Calculate the sample mean and sample deviation of the breakdown data.

Answer 1

Mean = 14.3679

S.D = 18.83

Explanation:

We are given the following data:

Time(minute)

0.15,0.75,0.96,1.35,2.87,3.19,4.01,4.62,4.88,6.43,7.41,8.04,8.24,12.86,31.63,32.61,33.98,36.18,72.83

Formula:

`Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observations}}`

`= \displaystyle(272.99)/(19) = 14.3679`

Formula:

`\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i - \bar{x})^2}{n-1}}`, where n is the total number of observations.

Sum of square of diffrences = 6386.57

S.D =
`\sqrt{\displaystyle(6386.57)/(18)} = 18.83`