Listed below are the durations (in hours) of a simple random sample of all fligh

Question

Listed below are the durations (in hours) of a simple random sample of all flights of a space shuttle program. Find the range, variance, and standard deviation for the sample data. Is the lowest duration time unusual? Why or why not? 75 90 240 199 168 265 195 371 253 233 388 332 221 243 0 The range of the sample data is hours. The variance of the sample data is (Round to one decimal place as needed.) The standard deviation of the sample data is hours (Round to one decimal place as needed.) Is the lowest duration time unusual? Why or why not? Yes, because it is more than two standard deviations below the mean. Yes, because the lowest value in a data set is usually an outlier. No, because it is within two standard deviations of the mean No, because the sample is random

Explanation / Answer

Range=max-min=388-75=313

Step 1: Find the mean. (X¯)

In this example:(X¯)= 233.7857

Step 2: Create the following table.

Step 3: Find the sum of numbers in the last column to get.

Sum(xi-X¯)^2=106816.3571

Step 4: Calculate variance using the below formula

Sum(xi-X¯)^2/n-1=106816.3571/13=8216.6429

Standard deviation=Sqrt(Variance)=90.6457

It is outlier so answer B is correct

data data-mean (data - mean)2 75 -158.7857 25212.8985245 90 -143.7857 20674.3275245 240 6.2143 38.61752449 199 -34.7857 1210.04492449 168 -65.7857 4327.75832449 265 31.2143 974.33252449 195 -38.7857 1504.33052449 371 137.2143 18827.7641245 253 19.2143 369.18932449 233 -0.7857 0.61732449 388 154.2143 23782.0503245 332 98.2143 9646.04872449 221 -12.7857 163.47412449 243 9.2143 84.90332449

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