91Ó°ÊÓ

Paired data is defined as sets of data acquired from same individual sample units at different periods of time.

Like, it usually includes data before and after a treatment.

Here, the same flight is being observed for outbound and return time on same route. So, it is paired data.

The dot plot represents that most of the differences of $outboundtime-returntime$are positive. It denotes that $outbondtime>returntime$.

Hence, the pilot's anticipation is correct.

Mean Difference $=Sumofdifferences/Numberofdifferences$

Mean = $$\begin{gathered} [33+ 5+....-5+ 4]÷12 \\ 121/12 \\ =10.083 \end{gathered}$$

Standard Deviation = ${(x_i-x\text{'})}^2$$$\begin{gathered} \sqrt{\underset{}{∑}{(x_i-x\text{'})}^2/(n-1)} \\ where{x}_i=individualdifferences,x\text{'}=meandifference,n=numberofsampleunits \end{gathered}$$

Similarly, by summing all the sum of deviations, we get

$$\begin{gathered} \sqrt{[{(33-10.083333333333)}^2+...+{(4-10.083333333333)}^2]/11} \\ =10.766 \end{gathered}$$

Standard deviation value denotes how scattered or spread the differences are around the mean standard difference, on an average.