Chapter 10.2, Problem 13HP

To determine

To find:Two listof data with the given condition.

Answer to Problem 13HP

The two list are

List 1	List 2
0	7
1	7.5
3	8
5	8.5
7	9
9	9
9	9.5
10	10
11	10.5
13	11
15	11.5
17	12
19	12
21	12.5
25	13

Explanation of Solution

Given information:The two list of data must have at least 15 values and of 10.One list should have arange of 25 and the other a range of 6.

Formula used:

For a given set of data

  $range=\text{largest}\text{value}-\text{least}\text{value}$

The Median of a given set of values is the middle value of the ordered set.

  $Median=\left\{\begin{array}{l}{\left(\frac{n+1}{2}\right)}^{th}\text{term,}\text{if}n\text{is}\text{odd}\\ \\ \frac{{\left(\frac{n}{2}\right)}^{th}\text{term}+{\left(\frac{n}{2}+1\right)}^{th}\text{term}}{2},\text{if}n\text{is}\text{even}\end{array}\right\}$

Calculation:

Since both the list have 15 values and the median must be 10, it means that

  $\begin{array}{l}median={\left(\frac{15+1}{2}\right)}^{th}term=10\\ 8^{th}term=10\end{array}$

Also for the first list the range is 25,that means

  $\begin{array}{l}range=\text{largest}\text{value}-\text{least}\text{value}=25\\ \\ \text{Therefore}\text{the}\text{difference}\text{of}\text{the}\text{first}\text{and}\text{last}\text{value}\text{of}\text{the}\text{table}\text{must}\text{be}\text{25}\text{and}\\ \text{Since}\text{the}\text{first}\text{value}\text{is}\text{lower}\text{than}\text{the}\text{median(10)}\text{and}\text{the}\text{last}\text{value}\text{is}\text{higher}\text{than}\text{the}\text{median}\left(10\right)\text{.}\\ \\ \text{The}\text{first}\text{and}\text{last}\text{value}\text{can}\text{be}\text{0}\text{and}\text{25}\text{respectively}\text{.}\end{array}$

Similarly for the second list the range is 6, that means

  $\begin{array}{l}range=\text{largest}\text{value}-\text{least}\text{value}=6\\ \\ \text{Therefore}\text{the}\text{difference}\text{of}\text{the}\text{first}\text{and}\text{last}\text{value}\text{of}\text{the}\text{table}\text{must}\text{be}6\text{and}\\ \text{Since}\text{the}\text{first}\text{value}\text{is}\text{lower}\text{than}\text{the}\text{median(10)}\text{and}\text{the}\text{last}\text{value}\text{is}\text{higher}\text{than}\text{the}\text{median}\left(10\right)\text{.}\\ \\ \text{The}\text{first}\text{and}\text{last}\text{value}\text{can}\text{be}7\text{and}\text{13}\text{respectively}\text{.}\end{array}$

Hence the two list are

List 1	List 2
0	7
1	7.5
3	8
5	8.5
7	9
9	9
9	9.5
10	10
11	10.5
13	11
15	11.5
17	12
19	12
21	12.5
25	13