Maths Support: Descriptive statistics

Question 1

Oxygen uptake values (mL/kg.min) for $\var{thismany}$ people working at $\var{100}$ watts on an exercise machine were:

Person	1	2	3	4	5
First attempt	$\var{r1[0]}$	$\var{r1[1]}$	$\var{r1[2]}$	$\var{r1[3]}$	$\var{r1[4]}$
Second attempt	$\var{r2[0]}$	$\var{r2[1]}$	$\var{r2[2]}$	$\var{r2[3]}$	$\var{r2[4]}$

Answer the following questions to 3 d.p.:

Find the mean and standard deviations of the difference between first and second attempts.

Calculate differences for second attempt – first attempt.

Please note that it is second attempt – first attempt

Mean of difference = question.score feedback.none Expected answer: (input as an exact decimal)

Standard deviation of difference = question.score feedback.none Expected answer: (input to 3 decimal places)

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The table of differences is given by:

Person	1	2	3	4	5
First attempt	$\var{r1[0]}$	$\var{r1[1]}$	$\var{r1[2]}$	$\var{r1[3]}$	$\var{r1[4]}$
Second attempt	$\var{r2[0]}$	$\var{r2[1]}$	$\var{r2[2]}$	$\var{r2[3]}$	$\var{r2[4]}$
Differences	$\var{d[0]}$	$\var{d[1]}$	$\var{d[2]}$	$\var{d[3]}$	$\var{d[4]}$

The mean of the differences is $\var{meandiff}$.

The variance $V$ of the differences is
\[\begin{eqnarray*} V&=&\frac{1}{4}\left(\simplify[]{({d[0]}^2+{d[1]}^2+{d[2]}^2+{d[3]}^2+{d[4]}^2)}-5\times \var{meandiff}^2\right)\\ &=&\var{variance(d,true)} \end{eqnarray*} \]
Hence we have the standard deviation = $\sqrt{V}=\var{stdiff}$ to 3 decimal places.

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Maths Support: Descriptive statistics

Question 1

Question 1

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