Question

Consider the following random sample of data: 13, 27, 28, 17, 21, 4, 10, 3, 108, 19 a) What is the median of the sample data? Round your response to 2 decimal places. b) If the outlier is removed, what is the median of the remaining sample data? ……..

Answer 1

The first step is to organize the number, as follows:

3, 4, 10, 13, 17, 19, 21, 27, 28, 108

The median is defined as the number which divides the group into two with the same number of terms. Because the number of terms is even, the median will be the mean of the two numbers in the middle, in the present case, 17 and 19.

`\text{median}=(17+19)/(2)=(36)/(2)=18`

From this, we conclude that the answer for the question a) is: 18.00

It was also possible to check that the number 108 is far bigger than any other. And for this reason, it is the outlier. If we remove it from the sample of data, we have the following sample:

3, 4, 10, 13, 17, 19, 21, 27, 28

Now, because the number of terms is odd, the one in the middle is the median. From this, we are able to conclude that the answer for question b) is: 17.00