Question

The following data show the number of months patients typically wait on a transplant list before getting surgery.

The data are ordered from smallest to largest. Calculate the mean and median.

$3;4;5;7;7;7;7;8;8;9;9;10;10;10;10;10;11;12;12;13;14;14;15;15;17;17;18;19;19;19;21;21;22;22;23;24;24;24;24$

Short answer

The mean is$13.9487179$ and the median is $13$, therefore we can say that the mean is somewhat higher than the median in this situation.

Step-by-step solution

Given

Here we have the data$3;4;5;7;7;7;7;8;8;9;9;10;10;10;10;10;11;12;12;13;14;14;15;15;17;17;18;19;19;19;21;21;22;22;23;24;24;24;24$

Solution

We have total observation, $n=39.$

So mean is Mean $=\overline{x}=\frac{n+1}{2}=\frac{544}{39}=13.9487179$ Since the data is being sorted in increasing order and there is $39$ observations the median is $\frac{n+1}{2}th$ observation so $\frac{n+1}{2}={20}^{\text{th}}$ observation is$13.$ Hence the median is $13$ .

Explanation of Solution

Thesamplemeanisjusttheaverageofthewholecollectionofdata,whereasthemedianisasingleobservationwithintheset.

Themedianandmeanimpactsarecalculatedusingsimplythenumberofobservationsinthedataandthesorteddata.

Outliers influence the mean, not the median, if the data contains them.

In the face of an outlier, it is always preferable to utilize the median rather than the mean.