In a data analysis, the breakdown time of an insulating fluid between electrodes at 34 kV is recorded. The times, in minutes, are as follows: 0.19, 0.78, 0.96, 1.31, 2.78, 3.16, 4.15, 4.67, 4.85, 6.50, 7.35, 8.01, 8.27, 12.06, 31.75, 32.52, 33.91, 36.71, and 72.89. Calculate the sample mean and sample standard deviation

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04-11-2019
Mathematics

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In a data analysis, the breakdown time of an insulating fluid between electrodes at 34 kV is recorded. The times, in minutes, are as follows: 0.19, 0.78, 0.96, 1.31, 2.78, 3.16, 4.15, 4.67, 4.85, 6.50, 7.35, 8.01, 8.27, 12.06, 31.75, 32.52, 33.91, 36.71, and 72.89. Calculate the sample mean and sample standard deviation

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ChiKesselman ChiKesselman · Answer 1 · 2019-11-05T09:08:58+01:00

Answer:

Sample mean = 14.3589

Sample standard deviation = 18.8804

Step-by-step explanation:

We are given the following information:

0.19, 0.78, 0.96, 1.31, 2.78, 3.16, 4.15, 4.67, 4.85, 6.50, 7.35, 8.01, 8.27, 12.06, 31.75, 32.52, 33.91, 36.71, 72.89

Formula:

[tex]\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}[/tex]

where [tex]x_i[/tex] are data points, [tex]\bar{x}[/tex] is the mean and n is the number of observations.

[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]

[tex]Mean =\displaystyle\frac{272.82}{19} = 14.3589[/tex]

Sum of squares of differences = 200.7590696 + 184.3878117 + 179.5317906 + 170.2750275 + 134.0720222 + 125.4164222 + 104.2226064 + 93.8757011 + 90.42008005 + 61.76305373 + 49.12534321 + 40.30913268 + 37.07528005 + 5.285159001 + 302.4487116 + 329.8238326 + 382.2436589 + 499.5695537 + 3425.884122 = 6416.4883

[tex]S.D = \sqrt{\frac{6416.4883}{18}} = 18.8804[/tex]