Chapter 13, Problem 5PT

To determine

To calculate: To find the measures of variation of the data

Answer to Problem 5PT

Median is $82$

Explanation of Solution

Given information: Table showing Ms. F’s 1^st period test grades

Science Test Grades
77	78	88	89	67	65	87	99
93	92	76	79	70	85	83	81

Formula Used:

There are four measures of variation

• Range
• Interquartile Range
• Variance
• Standard Deviation

Calculation:

Data is given as follows:

Science Test Grades
77	78	88	89	67	65	87	99
93	92	76	79	70	85	83	81

  $\begin{array}{ll}\text{ Stem }\hfill & \text{ Leaf }\hfill \\ 6\hfill & 5,7\hfill \\ 7\hfill & 0,6,7,8,9\hfill \\ 8\hfill & 1,3,5,7,8,9\hfill \\ 9\hfill & 2,3,9\hfill \end{array}$

Arranging the numbers in ascending order,

  $65,67,70,76,77,78,79,81,83,85,87,88,89,92,93,99$

Middle numbers are $81$ and $83$

Thus, median is calculated as

  $\begin{array}{l}Median=\frac{81+83}{2}\\ Median=\frac{164}{2}\\ Median=82\end{array}$

Conclusion:

Hence, median is $82$