The propagation of fatigue cracks in various aircraft parts has been the subject

Question

The propagation of fatigue cracks in various aircraft parts has been the subject of extensive study in recent years. The accompanying data consists of propagation lives (flight hours/10^4) to reach a given crack size in fastener holes intended for use in military aircraft. (a) Compute and compare the values of the sample mean x bar and median x ~. (Round your answers to four decimal places.) x bar = flight hours/10^4 x~ = flight hours/10^4 (b) By how much could the largest sample observation be decreased without affecting the value of the median? (Enter your answer to three decimal places.) flight hours/10^4

Explanation / Answer

b) Here median of the data set is 1.0225. The median for even number data set is nothing but the average of middle two values when data is arranged in increasing order.

Here median is = (1.0101 + 1.035) /2 = 1.0225

Now inorder to keep median unchanged we have to keep the largest value as small as 1.035. So the largest value in data set can be decreased by 1.364 - 1.035 = 0.329 so that the median would not change even the largest value is decreased.

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