Question

construct a stem-and-leaf diagram for the accompanying data, using two lines per stem.
21 49 35 31 40
31 38 36 29 39
22 39 30 23 34
33 37 39 30 40
complete the stem-and-leaf diagram with two lines per stem
(use ascending order.)

Explanation:

Step1: Identify stems and split leaves

First, list all data points: 21, 49, 35, 31, 40, 31, 38, 36, 29, 39, 22, 39, 30, 23, 34, 33, 37, 39, 30, 40.
Stems are tens digits: 2, 3, 4. For two lines per stem, split stem 2 into 2 (leaves 0 - 4) and 2 (leaves 5 - 9); stem 3 into 3 (leaves 0 - 4) and 3 (leaves 5 - 9); stem 4 into 4 (leaves 0 - 4) and 4 (leaves 5 - 9).

Step2: Sort leaves for each stem part

• Stem 2 (leaves 0 - 4): Data with tens=2 and ones 0 - 4: 21, 22, 23. Wait, no: 21 (ones=1), 22 (2), 23 (3), 29 is ones=9 (so stem 2, leaves 5 - 9). Wait, correct split: stem 2, first line (ones 0 - 4): 21 (1), 22 (2), 23 (3). Wait, 29 has ones=9, so stem 2, second line (ones 5 - 9): 29.
• Stem 3, first line (ones 0 - 4): 30, 30, 31, 31, 33, 34.
• Stem 3, second line (ones 5 - 9): 35, 36, 37, 38, 39, 39, 39.
• Stem 4, first line (ones 0 - 4): 40, 40.
• Stem 4, second line (ones 5 - 9): 49.

Now, sort leaves in ascending order for each stem part:

• Stem 2 (0 - 4): leaves 1, 2, 3 (from 21, 22, 23)
• Stem 2 (5 - 9): leaf 9 (from 29)
• Stem 3 (0 - 4): leaves 0, 0, 1, 1, 3, 4 (from 30, 30, 31, 31, 33, 34)
• Stem 3 (5 - 9): leaves 5, 6, 7, 8, 9, 9, 9 (from 35, 36, 37, 38, 39, 39, 39)
• Stem 4 (0 - 4): leaves 0, 0 (from 40, 40)
• Stem 4 (5 - 9): leaf 9 (from 49)

Answer:

Stem	Leaf
2	9
3	0 0 1 1 3 4
3	5 6 7 8 9 9 9
4	0 0
4	9