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

Explanation:

🆕 New Concept Discovered: Stem-and-Leaf Plots
Organizing data by place value

Step 1: Sort the data set

To easily construct or match a stem-and-leaf plot, we first list the given data values in ascending order:

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

Step 2: Group by stems (tens digits)

Next, we group the sorted numbers by their tens digit, which represents the "stem":

• Stem 1 (10s): \(13, 13, 14, 15, 15\) \(

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

• Stem 2 (20s): \(20, 21, 28, 29\) \(

ightarrow\) Leaves: \(0, 1, 8, 9\)

• Stem 3 (30s): \(36, 39\) \(

ightarrow\) Leaves: \(6, 9\)

• Stem 4 (40s): \(42\) \(

ightarrow\) Leaves: \(2\)

• Stem 5 (50s): \(52, 57, 57\) \(

ightarrow\) Leaves: \(2, 7, 7\)

Step 3: Match with the options

Now we compare our grouped stems and leaves to the given 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 plot that correctly represents the data set is X.

Answer:

X