Question

construct an ordered stem and leaf display for the following data:

100, 113, 106, 115
126, 90, 120, 131
114, 101, 112, 104
102, 127, 104, 133

complete the ordered stem and leaf diagram below.

Explanation:

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

Step 1: Group the data by stems

The dataset consists of the following 16 numbers:

$$ 100, 113, 106, 115, 126, 90, 120, 131, 114, 101, 112, 104, 102, 127, 104, 133 $$

We split each number into a stem (the leading digits) and a leaf (the final single digit).

• For numbers in the 90s, the stem is 9.
• For numbers in the 100s (100–109), the stem is 10.
• For numbers in the 110s (110–119), the stem is 11.
• For numbers in the 120s (120–129), the stem is 12.
• For numbers in the 130s (130–139), the stem is 13.

Let's group the values under their respective stems:

• Stem 9: \(90\)
• Stem 10: \(100, 106, 101, 104, 102, 104\)
• Stem 11: \(113, 115, 114, 112\)
• Stem 12: \(126, 120, 127\)
• Stem 13: \(131, 133\)

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Step 2: Order the leaves for each stem

To make an ordered stem-and-leaf plot, we arrange the leaves (the last digits) in ascending order from left to right for each stem:

• Stem 9:
• Value: \(90\) \(

ightarrow\) Leaf: 0

• Stem 10:
• Values: \(100, 101, 102, 104, 104, 106\) \(

ightarrow\) Leaves: 0, 1, 2, 4, 4, 6

• Stem 11:
• Values: \(112, 113, 114, 115\) \(

ightarrow\) Leaves: 2, 3, 4, 5

• Stem 12:
• Values: \(120, 126, 127\) \(

ightarrow\) Leaves: 0, 6, 7

• Stem 13:
• Values: \(131, 133\) \(

ightarrow\) Leaves: 1, 3

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Answer:

Complete the diagram by entering the ordered leaves into the boxes next to each stem:

• 9 | 0
• 10 | 012446
• 11 | 2345
• 12 | 067
• 13 | 13