Question

select the correct answer.

which stem and leaf plot represents the given data set?

57, 28, 15, 20, 21, 13, 36,
42, 14, 52, 15, 29, 39, 13, 57

w.
1 | 3, 4, 5
2 | 0, 1, 8, 9
3 | 6, 9
4 | 2
5 | 2, 7

x.
1 | 3, 3, 4, 5, 5
2 | 0, 1, 8, 9
3 | 6, 9
4 | 2
5 | 2, 7, 7

y.
1 | 3, 3, 5, 5, 5
2 | 0, 1, 8, 9
3 | 6, 9
4 | 2
5 | 2, 2, 7

z.
1 | 3, 3, 4, 5, 5
2 | 1, 8, 9
3 | 6, 9
4 | 2
5 | 2, 7, 7

• w
• x
• y
• z

Explanation:

🆕 New Concept Discovered: Stem-and-Leaf Plots
Organizing data by tens (stems) and ones (leaves).

Step 1: List and sort the data set

First, let's write down all the numbers from the given data set:

$$ 57, 28, 15, 20, 21, 13, 36, 42, 14, 52, 15, 29, 39, 13, 57 $$

Now, let's sort them in ascending order to make grouping easier:

$$ 13, 13, 14, 15, 15, 20, 21, 28, 29, 36, 39, 42, 52, 57, 57 $$

Step 2: Group by tens (stems) and ones (leaves)

A stem-and-leaf plot splits each two-digit number into a "stem" (the tens digit) and a "leaf" (the ones digit). Let's group our sorted data:

• Stem 1 (numbers in the 10s): \(13, 13, 14, 15, 15\)
• Leaves: \(3, 3, 4, 5, 5\)
• Stem 2 (numbers in the 20s): \(20, 21, 28, 29\)
• Leaves: \(0, 1, 8, 9\)
• Stem 3 (numbers in the 30s): \(36, 39\)
• Leaves: \(6, 9\)
• Stem 4 (numbers in the 40s): \(42\)
• Leaves: \(2\)
• Stem 5 (numbers in the 50s): \(52, 57, 57\)
• Leaves: \(2, 7, 7\)

Step 3: Match with the given options

Let's compare our groups to the choices:

• Row 1 (Stem 1): Must have leaves 3, 3, 4, 5, 5.
• Plot W has 3, 4, 5 (incorrect).
• Plot Y has 3, 3, 5, 5, 5 (incorrect).
• Plots X and Z have 3, 3, 4, 5, 5.

• Row 2 (Stem 2): Must have leaves 0, 1, 8, 9.
• Plot X has 0, 1, 8, 9 (correct).
• Plot Z has 1, 8, 9 (incorrect, missing the 0 for 20).

• Row 5 (Stem 5): Must have leaves 2, 7, 7.
• Plot X has 2, 7, 7 (correct).

Therefore, plot X is the correct representation.

Answer:

X