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: 29.7 49.9 30.8 28.5 28.8 26.7 33.5 29.8 24.0 31.5 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

Explanation / Answer

a) sample range = (max - min) = 49.9 - 24.0 = 25.9

b) mean = (29.7 + 49.9 + 30.8 + 28.5 + 28.8 + 26.7 + 33.5 + 29.8 + 24.0 + 31.5 ) / 10 = 31.32

sampl variance = [(29.7 - 31.32)2 + (49.9 - 31.32)2 + (30.8 - 31.32)2 + (28.5 - 31.32)2 + (28.8 - 31.32)2 + (26.7 - 31.32)2 + (33.5 - 31.32)2 + (29.8 - 31.32)2 + (24.0 - 31.32)2 + (31.5 - 31.32)2 ] / (10 - 1) = 49.38

c) sample standard deviation = sqrt(variance) = sqrt(49.38) = 7.03

d) s2 = (max - min) / 4 = (49.9 - 24.0) / 4 = 6.475

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