Chapter 1.3, Problem 79E

To determine

To calculate: the mean and interpret the result.

Answer to Problem 79E

Mean is 85

Out of 14 values, 7 are above mean and 7 are less than mean. Thus here mean is a balance point.

Explanation of Solution

Given:

86	84	91	75	78	80	74
87	76	%	82	90	98	95

Calculation:

The mean for Joe's first 14 quiz grades in a marking period is below:

  $\begin{array}{c}\text{Mean}=\overline{X}\\ =\frac{{\displaystyle \sum X_i}}{n}\\ =\frac{\text{sum}\text{of}\text{observations}}{n}\\ =\frac{x_1+x_2+x_3+\mathrm{...}+x_n}{n}\\ =\frac{86+87+84+76+91+96+75+82+78+90+80+98+74+93}{14}\\ =\frac{1190}{14}\\ \text{Mean}=85\end{array}$

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". From this we interpret that out of 14 values, 7 are above mean and 7 are less than mean. Thus here mean is a balance point.

Conclusion:

Therefore, mean is 85

Out of 14 values, 7 are above mean and 7 are less than mean. Thus here mean is a balance point.