Chapter 1.3, Problem 80E

To determine

To find: Calculate the mean.

Answer to Problem 80E

Mean is 305.86.

Explanation of Solution

Given:

  $306+305+315+303+318+309+285$

Calculation:

The mean for the 7 defensive linemen is given below:

  $\begin{array}{l}\text{Mean=}\overline{X}\\ =\frac{{\displaystyle \sum X_i}}{N}=\frac{x_1+x_2+x_3+\mathrm{.....}+x_n}{n}\\ \text{ =}\frac{306+305+315+303+318+309+285}{7}\\ =\frac{\text{sum of observations}}{n}\text{ =}\frac{2141}{7}\\ \text{Mean=305}\text{.86}\end{array}$

The mean tells us how large each observation in the data set would be if the total were split equally among all the observations i.e. mean is a "fair share" or a balance point. From this have noticed that there are 3 observations below mean and 4 observations above mean. If we leave out the smallest (285) observation the mean would be 309.33 which is the balance point of the data. One observation brings down the value of mean by 3.47 points. Now with 309.33 mean of six observations (after leaving the extreme observation) three observations are above and three observations are below 309.33.

Conclusion: “Thus, we conclude that due to presence of extreme value mean gets affected. Mean is sensitive to outliers.”