Back-to-back stem-and-leaf plot worksheet for practicing data visualization.

Let’s solve each back-to-back stem-and-leaf plot step by step.

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Problem 1:

Data for A:
55, 39, 33, 21, 57, 40, 33, 52, 47, 24, 31, 26

Data for B:
27, 59, 22, 47, 33, 56, 27, 24, 39, 43, 27, 53

We need to make a back-to-back stem-and-leaf plot. The “stem” is the tens digit, and the “leaf” is the ones digit.

First, list all numbers with their stems:

For A:
- 2 | 1, 4, 6 → from 21, 24, 26
- 3 | 1, 3, 3, 9 → from 31, 33, 33, 39
- 4 | 0, 7 → from 40, 47
- 5 | 2, 5, 7 → from 52, 55, 57

Wait — let’s sort them properly.

Actually, better to sort each group first.

Sorted A:
21, 24, 26, 31, 33, 33, 39, 40, 47, 52, 55, 57

Sorted B:
22, 24, 27, 27, 27, 33, 39, 43, 47, 53, 56, 59

Now build the plot.

Stem 2:
Leaf B (left): 2, 4, 7, 7, 7 → but we write leaves in order, so 2, 4, 7, 7, 7
Leaf A (right): 1, 4, 6

But in back-to-back, Leaf B goes on left, sorted ascending; Leaf A on right, also sorted ascending.

So:

Stem 2:
B: 2 4 7 7 7
A: 1 4 6

Stem 3:
B: 3 9
A: 1 3 3 9

Stem 4:
B: 3 7
A: 0 7

Stem 5:
B: 3 6 9
A: 2 5 7

Now, key says: 2|6 = ? That means stem 2, leaf 6 → which is 26. So key is 26.

Wait — in the problem, it says “Key: 2|6 = ___”

In our data, 26 is in set A. So yes, 2|6 means 26.

So for Problem 1, Key: 2|6 = 26

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Problem 2:

Data for A:
405, 418, 411, 397, 405, 391, 417, 390, 405, 392

Data for B:
417, 395, 405, 417, 392, 393, 406, 418, 399, 401

These are 3-digit numbers. The key says: 39|7 = ?

That suggests stem is hundreds and tens, leaf is units.

So 39|7 means 397.

Let’s verify.

Sort A:

390, 391, 392, 397, 405, 405, 405, 411, 417, 418

Sort B:

392, 393, 395, 399, 401, 405, 406, 417, 417, 418

Now, stems will be 39, 40, 41.

Stem 39:
B leaves: 2, 3, 5, 9 → from 392, 393, 395, 399
A leaves: 0, 1, 2, 7 → from 390, 391, 392, 397

Stem 40:
B leaves: 1, 5, 6 → from 401, 405, 406
A leaves: 5, 5, 5 → from 405, 405, 405

Stem 41:
B leaves: 7, 7, 8 → from 417, 417, 418
A leaves: 1, 7, 8 → from 411, 417, 418

Key: 39|7 = 397 → correct.

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Problem 3:

Data for A:
6.5, 8.9, 7.2, 8.2, 6.2, 7.7, 8.2, 6.9, 7.5

Data for B:
8.1, 7.8, 6.7, 7.6, 8.1, 6.3, 7.5, 8.2, 6.7

These are decimals. Key says: 8|2 = ?

Probably means 8.2 — so stem is whole number, leaf is tenths digit.

So 8|2 = 8.2

Let’s confirm.

Sort A:

6.2, 6.5, 6.9, 7.2, 7.5, 7.7, 8.2, 8.2, 8.9

Sort B:

6.3, 6.7, 6.7, 7.5, 7.6, 7.8, 8.1, 8.1, 8.2

Stems: 6, 7, 8

Stem 6:
B leaves: 3, 7, 7 → from 6.3, 6.7, 6.7
A leaves: 2, 5, 9 → from 6.2, 6.5, 6.9

Stem 7:
B leaves: 5, 6, 8 → from 7.5, 7.6, 7.8
A leaves: 2, 5, 7 → from 7.2, 7.5, 7.7

Stem 8:
B leaves: 1, 1, 2 → from 8.1, 8.1, 8.2
A leaves: 2, 2, 9 → from 8.2, 8.2, 8.9

Key: 8|2 = 8.2 → correct.

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Final Answers:

For each problem, fill in the key as shown.

Problem 1 Key: 2|6 = 26
Problem 2 Key: 39|7 = 397
Problem 3 Key: 8|2 = 8.2

Also, you would fill in the plots as above, but since the question only asks for the keys (based on the blanks), we provide those.

Looking back at the worksheet, under each plot there is a “Key: __|__ = _____” blank.

So we just need to fill those.

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Final Answer:
1) 26
2) 397
3) 8.2