Question

the accompanying data set lists diastolic blood - pressure measurements (mm hg) of females. all of the values are even numbers. construct a stemplot. identify the two values that are closest to the middle when the data are sorted in order from lowest to highest. (these values are often used to find the median.) 72 74 88 88 74 66 76 70 96 90 88 70 72 68 60 66 86 90 72 68 60 construct the stemplot.

Explanation:

Step1: Determine the stems

The tens - digit of each data value will be the stem. The possible stems are 6, 7, 8, 9.

Step2: List the leaves

For stem 6: The data values with 6 as the tens - digit are 60, 66, 68, 68. So the leaves are 0, 6, 8, 8.
For stem 7: The data values with 7 as the tens - digit are 70, 72, 72, 72, 74, 74, 76. So the leaves are 0, 2, 2, 2, 4, 4, 6.
For stem 8: The data values with 8 as the tens - digit are 86, 88, 88. So the leaves are 6, 8, 8.
For stem 9: The data values with 9 as the tens - digit are 90, 96. So the leaves are 0, 6.

Step3: Construct the stemplot

We write the stems on the left - hand side and the corresponding leaves on the right - hand side, in ascending order.
Stemplot:
6 | 0 6 8 8
7 | 0 2 2 2 4 4 6
8 | 6 8 8
9 | 0 6

Step4: Find the middle values

There are 20 data values. Since \(n = 20\) (an even number), the median is the average of the \(\frac{n}{2}=10\)th and \((\frac{n}{2}+1)=11\)th ordered data values.
Counting the leaves from the stemplot, the 10th value is 72 and the 11th value is 74.

Answer:

Stemplot:
6 | 0 6 8 8
7 | 0 2 2 2 4 4 6
8 | 6 8 8
9 | 0 6
Values closest to the middle: 72, 74