An article reported the following data on oxygen consumption (mL/kg/min) for a sample of ten firefighters performing a fire-suppression simulation: 28.6 49.4 30.3 28.2 28.9 26.4 33.8 29.9 23.5 30.2Compute the following. (Round your answers to four decimal places.) a. The sample range mL/kg/minb. The sample variance s2 from the definition (i.e., by first computing deviations, then squaring them, etc.) mL2/kg2/min2c. The sample standard deviation mL/kg/mind. s2 using the shortcut method mL2/kg2/min

Answer :

Answer:

a) The sample range 25.9 [tex]ml\slash kg\slash \min[/tex]

b) The sample variance is 49.344 [tex]ml^2 \slash kg^2 \slash min^2[/tex]

c) The sample standard deviation 7.0245 [tex]ml\slash kg\slash \min[/tex]                  

Step-by-step explanation:

We are given the following data on oxygen consumption (mL/kg/min):

28.6, 49.4, 30.3, 28.2, 28.9, 26.4, 33.8, 29.9, 23.5, 30.2

a) The sample range

Range = Maximum - Minimum

[tex]\text{Range} = 49.4 - 23.5 = 25.9[/tex]

The sample range 25.9 [tex]ml\slash kg\slash \min[/tex]

b) The sample variance

[tex]\text{Variance} = \displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}[/tex]  

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

[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]

[tex]Mean =\displaystyle\frac{309.2}{10} = 30.92[/tex]

Sum of squares of differences =

5.3824 + 341.5104 + 0.3844 + 7.3984 + 4.0804 + 20.4304 + 8.2944 + 1.0404 + 55.0564 + 0.5184 = 444.096

[tex]s^2 = \dfrac{444.096}{9} = 49.344[/tex]

The sample variance is 49.344 [tex]ml^2 \slash kg^2 \slash min^2[/tex]

c)  The sample standard deviation

It is the square root of sample variance.

[tex]s = \sqrt{s^2} = \sqrt{49.344} = 7.0245[/tex]

The sample standard deviation 7.0245 [tex]ml\slash kg\slash \min[/tex]

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