An article reported the following data on oxygen consumption (mL/kg/min) for a s

Question

An article reported the following data on oxygen consumption (mL/kg/min) for a sample of ten firefighters performing a fire-suppression simulation: 28.9 49.3 30.2 28.6 26.8 33.8 29.8 23.0 31.1 Compute the following. (Round your answers to four decimal places.) (a) The sample range mL/kg/min (b) The sample variance s^2 from the definition (i.e., by first computing deviations, then squaring them, etc.) mL^2/kg^2/min^2 (c) The sample standard deviation mL/kg/min (d) s^2 using the shortcut method mL^2/kg^2/min^2 Each of a sample of four home mortgages is classified as fixed rate (F) or variable rate (V), (Enter your answers in set notation. Enter EMPTY or 0 for (a) What are the 16 outcomes in S? S =

Explanation / Answer

Mean = Sum of observations/ Count of observations
Mean = (28.9 + 49.3 + 30.2 + 28.6 + 28.6 + 26.8 + 33.8 + 29.8 + 23 + 31.1 / 10) = 31.01
Variance
Step 1: Add them up
28.9 + 49.3 + 30.2 + 28.6 + 28.6 + 26.8 + 33.8 + 29.8 + 23 + 31.1 = 310.1
Step 2: Square your answer
310.1*310.1 =96162.01
…and divide by the number of items. We have 10 items , 96162.01/10 = 9616.201
Set this number aside for a moment.
Step 3: Take your set of original numbers from Step 1, and square them individually this time
28.9^2 + 49.3^2 + 30.2^2 + 28.6^2 + 28.6^2 + 26.8^2 + 33.8^2 + 29.8^2 + 23^2 + 31.1^2 = 10058.59
Step 4: Subtract the amount in Step 2 from the amount in Step 3
10058.59 - 9616.201 = 442.389
Step 5: Subtract 1 from the number of items in your data set, 10 - 1 = 9
Step 6: Divide the number in Step 4 by the number in Step 5. This gives you the variance
442.389 / 9 = 49.1543
Step 7: Take the square root of your answer from Step 6. This gives you the standard deviation
7.011

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