91Ó°ÊÓ

The weights (in pounds) were $321,285,300,285,286,293,298$

Number of observations, $n=7$

The total of all observations divided by the number of observations is the observation means. The median of a distribution organized in ascending order is the midway.

For the seven defensive linemen, the median is.

$M=306$= Median

The median is the distribution's middle. The number of observations in which half are smaller and half are greater. About half of the observations in the data set are above $306$ and the other half are below $306$Therefore, the median is $306$

Weighs $265$ pounds instead of $285$ pounds.

If $265$ had been used instead of $285$ in the sample, the mean and median would have been:

Mean $$\begin{gathered} \overline{x}=\frac{sumofobservations}{n} \\ \overline{x}=\frac{x_1+x_2+x_3+.....+x_n}{n} \\ \overline{x}=\frac{\mathrm{Î\pounds }Xi}{N} \\ \mathrm{Î\pounds }X=\frac{306+305+315+303+318+309+265}{N} \\ =\frac{2121}{7} \\ \overline{X}=303 \end{gathered}$$

Median= $M=306$

We can see from the preceding computation that when the extreme value changes, the means change as well, but the median stays the same. This means that the mean, but not the median, is sensitive to extreme values in the data. If one of the variables is changed from $285$ pounds to $265$ pounds, the mean will fall. Because $285$ is the smallest number in the data set, if one of the values stays the same from $285$ to $265$ pounds, the median will not be affected. Outliers influence the mean (because it decreases), but outliers have no effect on the median (also called robust). The mean decreases, the median is unaffected and the property is robust.