Chapter 13, Problem 3PT

(a)

To determine

To calculate: To display the data in a stem and leaf plot

Answer to Problem 3PT

Data is represented in stem and leaf plot

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:

A stem and leaf plot is a special table where each data value is split into a “stem” (first digit(s)) and a “leaf” (usually the last digit)

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

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

Conclusion:

Hence, data is represented in stem and leaf plot

(b)

To determine

To calculate: To find the median test grade

Answer to Problem 3PT

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:

Median is the middle number in a sorted ascending or descending list of numbers

When the list of number is odd, median is middle number

When the list of numbers is even, median is average of two middle numbers

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

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 $82$

(c)

To determine

To calculate: To find the interval do the most of grades occur

Answer to Problem 3PT

The interval with most grades is $76-80$

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

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

Intervals are

  $66-70$ , $71-75$ , $76-80$ , $81-85$ , $86-90$ , $91-95$ , $96-100$

Intervals	Numbers	Count
$66-70$	65, 67	2
$71-75$	70	1
$76-80$	76, 77, 78, 79	4
$81-85$	81, 83, 85	3
$86-90$	87, 88, 89	3
$91-95$	92, 93	2
$96-100$	99	1

Thus, interval with most grades is $76-80$

Conclusion:

Hence, the required interval is $76-80$