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: Group the data by the tens place

To create a stem-and-leaf plot, we group the numbers by their tens digit (the "stem") and list their ones digits (the "leaves") in ascending order.

Our data set:

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

Let's group them by their tens digit:

• 10s (Stem 1): \(15, 13, 14, 15, 13\)
• 20s (Stem 2): \(28, 20, 21, 29\)
• 30s (Stem 3): \(36, 39\)
• 40s (Stem 4): \(42\)
• 50s (Stem 5): \(57, 52, 57\)

Step 2: Order the leaves for each stem

Now, we sort the ones digits (leaves) for each stem in ascending order, making sure to include duplicate values:

• Stem 1: \(3, 3, 4, 5, 5\)
• Stem 2: \(0, 1, 8, 9\)
• Stem 3: \(6, 9\)
• Stem 4: \(2\)
• Stem 5: \(2, 7, 7\)

Step 3: Match with the given options

Let's compare our sorted stems and leaves with the choices:

• W: Stem 1 has leaves \(3, 4, 5\) (incorrect, missing duplicates).
• X:
• Stem 1: \(3, 3, 4, 5, 5\) (correct)
• Stem 2: \(0, 1, 8, 9\) (correct)
• Stem 3: \(6, 9\) (correct)
• Stem 4: \(2\) (correct)
• Stem 5: \(2, 7, 7\) (correct)
• Y: Stem 1 has leaves \(3, 3, 5, 5, 5\) (incorrect).
• Z: Stem 2 has leaves \(1, 8, 9\) (incorrect, missing \(0\)).

The correct plot is X.

Answer:

X