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Chapter 2: Q. 2.26 (page 102)

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

Expert verified

The mean is13.9487179 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

01

Given

Here we have the data3;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

02

Solution

We have total observation, n=39.

So mean is Mean =x炉=n+12=54439=13.9487179 Since the data is being sorted in increasing order and there is 39 observations the median is n+12th observation so n+12=20th observation is13. Hence the median is 13 .

03

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.

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