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.) 80 72 76 84 62 70 68 66 76 82 78 72 90 78 96 70 68 88 76 construct the stemplot.

Explanation:

Step1: Identify stem - digit

The data values range from 62 - 96. We will use the tens - digit as the stem.

Step2: List stems

The possible stems are 6, 7, 8, 9.

Step3: List leaves

For stem 6: The data values with 6 as the tens - digit are 62, 62, 66, 68. So the leaves are 2, 2, 6, 8.
For stem 7: The data values are 70, 70, 72, 72, 76, 76, 76, 78, 78. So the leaves are 0, 0, 2, 2, 6, 6, 6, 8, 8.
For stem 8: The data values are 80, 82, 84, 88. So the leaves are 0, 2, 4, 8.
For stem 9: The data values are 90, 94, 96. So the leaves are 0, 4, 6.

Step4: Construct stemplot

6 | 2 2 6 8
7 | 0 0 2 2 6 6 6 8 8
8 | 0 2 4 8
9 | 0 4 6

To find the two values closest to the middle:
There are \(n = 20\) data points. The median position for \(n = 20\) (an even - numbered data set) is \(\frac{n}{2}=10\) and \(\frac{n}{2}+ 1 = 11\) when the data is ordered.
Counting the ordered data from the stemplot, the 10th and 11th values are 76 and 76.

Answer:

The stemplot is:
6 | 2 2 6 8
7 | 0 0 2 2 6 6 6 8 8
8 | 0 2 4 8
9 | 0 4 6
The two values closest to the middle are 76 and 76.