Question

In Applied Life Data Analysis (Wiley, 1982), Wayne Nelson presents the breakdown time of an insulating fluid between electrodes at 34 kV. The times, in minutes, are as follows: 0.15, 0.89, 1.11, 1.46, 2.78, 3.12, 4.30, 4.59, 4.92, 6.42, 7.20, 8.04, 8.21, 12.13, 31.86, 32.53, 33.82, 36.60, and 72.99. Calculate the sample mean and sample standard deviation. Round the answers to 3 decimal places.

Answer 1

Answer:

18.375

Explanation:

Mean = total of measured values / no of elements of sample

Total = .15 + .89 +1.11+1.46 +2.78 + 3.12 + 4.30 + 4.59 + 4.92 + 6.42 + 7.20+8.04+8.21+12.13+31.86+32.53+33.82+36.60+ 72.99

= 273.03

Mean = 273 .03 / 19

= 14.37

( .15 - 14.37 )² +( 0.89 - 14.37 )²+( 1.11- 14.37 )²+( 1.46 - 14.37 )²+( 2.78 - 14.37 )²+( 3.12 - 14.37 )²+( 4.30 - 14.37 )²+( 4.59 - 14.37 )²+( 4.92 - 14.37 )²+( 6.42 - 14.37 )²+( 7.20 - 14.37 )²+( 8.04 - 14.37 )²+( 8.21 - 14.37 )²+( 12.13 - 14.37 )²+( 31.86 - 14.37 )²+( 32.53 - 14.37 )²+( 33.82 - 14.37 )²+( 36.60 - 14.37 )²+( 72.99 - 14.37 )²

= 202.20 +181.71+ 175.82 + 166.66+ 134.32 + 126.56 + 101.40 +95.64 + 89.30 +63.20 +51.40 +40.06 +37.94+5.01 +305.90 +329.78 +378.30 +494.17 +3436.30

=6415.67

Standard deviation =

$\sqrt{\frac{6415.67}{19} }$

= 18.375