Chapter 2, Problem 2.68RE

To determine

To find: the percent of the numbers in the list fall above the median.

Explanation of Solution

Calculation:

For example

1, 1, 10, 1, 1, 1, 1, 1, 1, 1

  $\begin{array}{c}\mu =\frac{{\displaystyle \sum x}}{n}\\ =\frac{1+1+10+1+1+1+1+1+1+1}{10}\\ =\frac{19}{10}\\ =1.9\end{array}$

Therefore it is observed that there is only digit 10 is above the mean, which associates with 10%. In this example median would be less than 1 and therefore also 10% lies above the median.

Although this would be not happened for all the list for example

1, 1, 1, 1, 1, 2, 2, 2, 2, 10

From this example the median of this list is 1.5 and then it is observed that 50 percent of the data is above the median.