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.

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$$\begin{array}{cccccccccc} 78 & 87 & 91 & 85 & 97 & 102 & 73 & 90 & 110 & 105 \\\\ 94 & 85 & 81 & 95 & 77 & 106 & 84 & 111 & 83 & 92 \\\\ 79 & 81 & 90 & 88 & 100 & 85 & 89 & 101 & 83 & 120 \\\\ 88 & 95 & 78 & 74 & 105 & 85 & 87 & 92 & 114 & 83 \\end{array}$$

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Explanation:

🆕 New Concept Discovered: Stem-and-Leaf Plots
Organizing data by splitting values into stems and leaves.

Step 1: Identify the range of the data

Find the minimum and maximum values in the dataset to determine the stems:

• Minimum value: \(73\)
• Maximum value: \(120\)

The stems will represent the tens (and hundreds) digits, ranging from \(7\) (for the \(70\)s) up to \(12\) (for the \(120\)s).

Step 2: Group and sort the data by stems

Group the data values by their leading digit(s) and list the units digit (leaves) in ascending order:

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

Step 3: Compare with the given options

• The first option only goes up to stem \(10\), omitting the values in the \(110\)s and \(120\)s (such as \(110, 111, 114, 120\)).
• The second option correctly lists all stems from \(7\) to \(12\) and includes all corresponding leaves in ordered sequence.

Answer:

The correct choice is the second option (on the right):

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