Question

the diastolic blood pressures for a sample of patients at a clinic were as follows. the measurements are in mmhg. construct a stem-and-leaf diagram for the given data.

78 87 91 85 97 102 73 90 110 105
94 85 81 95 77 106 84 111 83 92
79 81 96 88 100 85 89 101 83 120
88 95 78 74 105 85 87 92 114 83

Explanation:

🆕 New Concept Discovered: Stem-and-Leaf Plots
Organizing numerical data by splitting each value into a "stem" and a "leaf"

Step 1: Identify the range of the data

To determine the stems, we look at the minimum and maximum values in the dataset:

• Minimum value: \(73\) (stem is \(7\), leaf is \(3\))
• Maximum value: \(120\) (stem is \(12\), leaf is \(0\))

This means our stems must range from \(7\) to \(12\).

Step 2: Group and sort the data by stems

We group the data points by their leading digit(s) (the tens and hundreds places) and sort the units digits (leaves) in ascending order:

• Stem 7 (values in the 70s): \(73, 74, 77, 78, 78, 79\)
• Leaves: \(3, 4, 7, 8, 8, 9\)
• Stem 8 (values in the 80s): \(81, 81, 83, 83, 83, 84, 85, 85, 85, 85, 87, 87, 88, 88, 89\)
• Leaves: \(1, 1, 3, 3, 3, 4, 5, 5, 5, 5, 7, 7, 8, 8, 9\)
• Stem 9 (values in the 90s): \(90, 91, 92, 92, 94, 95, 95, 96, 97\)
• Leaves: \(0, 1, 2, 2, 4, 5, 5, 6, 7\)
• Stem 10 (values in the 100s): \(100, 101, 102, 105, 105, 106\)
• Leaves: \(0, 1, 2, 5, 5, 6\)
• Stem 11 (values in the 110s): \(110, 111, 114\)
• Leaves: \(0, 1, 4\)
• Stem 12 (values in the 120s): \(120\)
• Leaves: \(0\)

Step 3: Match with the given options

• The first option only goes up to stem \(10\), completely omitting the data points in the 110s and 120s (such as \(110, 111, 114, 120\)).
• The second option correctly lists all stems from \(7\) to \(12\) and matches our sorted leaves perfectly.

Answer:

The correct stem-and-leaf diagram is the second option:

 Stem | Leaf
-----------------------------
    7 | 3 4 7 8 8 9
    8 | 1 1 3 3 3 4 5 5 5 5 7 7 8 8 9
    9 | 0 1 2 2 4 5 5 6 7
   10 | 0 1 2 5 5 6
   11 | 0 1 4
   12 | 0