Q 79. - The Practice of Statistics for AP

Question

Quiz grades Joey’s first $14$ quiz grades in a marking period were 

86	84	91	75	78	80	74
87	76	96	82	90	98	93

Calculate the mean. Show your work. Interpret your result in context. 

Step-by-Step Solution

Answer

Mean is $85$ Out of $14$values,$7$ are above mean and $7$ are less than mean. Thus here mean is a balance point.

Step 1: Given information

Given: 

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

Step 2: Concept

The count of "average" is a single number that is taken as a representative of a list of numbers. Thus, the sum of the numbers divided by the count of numbers in the list is the average.

Step 3: Calculation

The following is the average of Joe's first 14 quiz grades in a marking period:

Mean = $\overline{X}$

$$\begin{gathered} = \frac{\Sigma xi}{n} \\ = \frac{sum of observations}{n} \\ = \frac{x_1+x_2+x_3+.....+x_n}{n} \\ = \frac{86+87+84+76+91+96+75+82+78+90+80+98+74+93}{14} \\ =\frac{1190}{14} \end{gathered}$$

Mean =$85$

The mean shows us how big each observation in the data set would be if the total was distributed evenly across all of them, i.e. the mean is a "fair share." We may deduce that $7$ of the $14$ numbers are greater than the mean and $7$ are less than the mean. As a result, the mean is a point of equilibrium.

Therefore, mean is $85$