Mathematics: The following data are the joint temperatures of the O-rings (oF) for each test firing or actual launch of the space shuttle rocket motor (from Presidential Commission on the Space Shuttle Challenger Accident, Vol. 1, pp. 129-131) 84, 49, 61, 40, 83, 67, 45, 66, 70, 69, 80, 58, 68, 60, 67, 72, 73, 70, 57, 63, 70, 78, 52, 67, 53, 67, 75, 61, 70, 81, 76, 79, 75, 76, 58, 31. Set aside the smallest observation (31oF) and re-compute the sample mean and sample standard deviation. Note the difference from

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The following data are the joint temperatures

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20.01.2022

Sample mean = 65.86

Sample standard deviation, s = 12.16

Step-by-step explanation:

We are given the following in the question:

84, 49, 61, 40, 83, 67, 45, 66, 70, 69, 80, 58, 68, 60, 67, 72, 73, 70, 57, 63, 70, 78, 52, 67, 53, 67, 75, 61, 70, 81, 76, 79, 75, 76, 58, 31

Formula:

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

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

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

$\bar{x} =\displaystyle\frac{2371}{36} = 65.86$

Sum of squares of differences = 5174.30

$s = \sqrt{\dfrac{5174.30}{35}} = 12.16$

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