Stem-and-Leaf Plots Worksheets - Free Printable

Let's solve both problems step by step and create back-to-back stem-and-leaf plots for the given data.

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🔷 What is a Back-to-Back Stem-and-Leaf Plot?

A back-to-back stem-and-leaf plot compares two sets of data (Group A and Group B) by using the same "stem" (the tens or hundreds digit), with "leaves" (the units digits) on either side:
- Left side: Data from Group B
- Right side: Data from Group A

We sort the leaves in ascending order for each stem.

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## ✔ Problem 1

Given Data:

| A | 66 | 29 | 38 | 20 | 86 | 67 | 31 | 84 | 25 | 83 |
|---|----|----|----|----|----|----|----|----|----|----|
| B | 39 | 26 | 80 | 67 | 27 | 32 | 88 | 23 | 82 | 21 |

Step 1: Sort the data

#### Group A (sorted):
20, 25, 29, 31, 38, 66, 67, 83, 84, 86

#### Group B (sorted):
21, 23, 26, 27, 32, 39, 67, 80, 82, 88

Step 2: Determine stems

The numbers range from 20 to 88, so stems will be the tens digits:
→ 2, 3, 6, 8

We'll list stems in increasing order.

Step 3: Build the plot

For each stem, write the leaves (units digits) for both groups.

| Leaf B | Stem | Leaf A |
|--------|------|--------|
| | 2 | 0 5 9 |
| | 3 | 1 8 |
| 7 2 9 | 6 | 6 7 |
| 8 2 0 | 8 | 3 4 6 |

Wait — let's do it carefully.

#### For each stem:

- Stem 2:
- A: 20, 25, 29 → leaves: 0, 5, 9
- B: 21, 23, 26, 27 → leaves: 1, 3, 6, 7

- Stem 3:
- A: 31, 38 → leaves: 1, 8
- B: 32, 39 → leaves: 2, 9

- Stem 6:
- A: 66, 67 → leaves: 6, 7
- B: 67 → leaf: 7

- Stem 8:
- A: 83, 84, 86 → leaves: 3, 4, 6
- B: 80, 82, 88 → leaves: 0, 2, 8

Now arrange them properly in the table:

| Leaf B | Stem | Leaf A |
|--------|------|--------|
| 7 6 3 1 | 2 | 0 5 9 |
| 9 2 | 3 | 1 8 |
| 7 | 6 | 6 7 |
| 8 2 0 | 8 | 3 4 6 |

> Note: Leaves are written in ascending order from the stem outward.

But we need to align the leaves correctly. Let’s format it clearly:

```
Leaf B | Stem | Leaf A
---------------|------|--------
7 6 3 1 | 2 | 0 5 9
9 2 | 3 | 1 8
7 | 6 | 6 7
8 2 0 | 8 | 3 4 6
```

Wait — actually, in back-to-back plots, the B leaves are reversed in order (from right to left) so that they increase from the stem outward.

So for each stem, we list the B leaves in descending order on the left, and A leaves in ascending order on the right.

✔ Corrected version:

| Leaf B (descending) | Stem | Leaf A (ascending) |
|---------------------|------|--------------------|
| 7 6 3 1 | 2 | 0 5 9 |
| 9 2 | 3 | 1 8 |
| 7 | 6 | 6 7 |
| 8 2 0 | 8 | 3 4 6 |

Wait — let's double-check:

- Stem 2:
B: 21, 23, 26, 27 → leaves: 1, 3, 6, 7 → descending: 7, 6, 3, 1
A: 20, 25, 29 → leaves: 0, 5, 9 → ascending: 0, 5, 9 ✔

- Stem 3:
B: 32, 39 → leaves: 2, 9 → descending: 9, 2
A: 31, 38 → leaves: 1, 8 → ascending: 1, 8 ✔

- Stem 6:
B: 67 → leaf: 7 → descending: 7
A: 66, 67 → leaves: 6, 7 → ascending: 6, 7 ✔

- Stem 8:
B: 80, 82, 88 → leaves: 0, 2, 8 → descending: 8, 2, 0
A: 83, 84, 86 → leaves: 3, 4, 6 → ascending: 3, 4, 6 ✔

So final plot:

```
Leaf B | Stem | Leaf A
------------|------|--------
7 6 3 1 | 2 | 0 5 9
9 2 | 3 | 1 8
7 | 6 | 6 7
8 2 0 | 8 | 3 4 6
```

Key: `3|8 = ___`

This means: stem 3, leaf 8 → number is 38

So:
Key: 3|8 = 38

✔ Final Answer for Problem 1:

```
Leaf B | Stem | Leaf A
------------|------|--------
7 6 3 1 | 2 | 0 5 9
9 2 | 3 | 1 8
7 | 6 | 6 7
8 2 0 | 8 | 3 4 6
```

Key: 3|8 = 38

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## ✔ Problem 2

Given Data:

| A | 502 | 215 | 765 | 219 | 103 | 761 | 210 | 217 | 504 | 105 |
|---|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|
| B | 762 | 509 | 213 | 767 | 104 | 505 | 109 | 213 | 506 | 217 |

Step 1: Sort the data

#### Group A (sorted):
103, 105, 210, 215, 217, 219, 502, 504, 761, 765

#### Group B (sorted):
104, 109, 213, 213, 217, 505, 506, 509, 762, 767

Step 2: Determine stems

These are three-digit numbers, so stems are based on hundreds and tens digits.

Look at the numbers:
- 103 → stem: 10
- 210 → stem: 21
- 502 → stem: 50
- 761 → stem: 76

So stems: 10, 21, 50, 76

We’ll use these as the stems.

Step 3: Extract leaves

Leaves are the last digit (units place).

#### For each stem:

- Stem 10:
A: 103, 105 → leaves: 3, 5
B: 104, 109 → leaves: 4, 9

- Stem 21:
A: 210, 215, 217, 219 → leaves: 0, 5, 7, 9
B: 213, 213, 217 → leaves: 3, 3, 7

- Stem 50:
A: 502, 504 → leaves: 2, 4
B: 505, 506, 509 → leaves: 5, 6, 9

- Stem 76:
A: 761, 765 → leaves: 1, 5
B: 762, 767 → leaves: 2, 7

Now build the back-to-back plot.

We want:
- Left side: B leaves in descending order
- Right side: A leaves in ascending order

Let’s fill in:

| Leaf B (descending) | Stem | Leaf A (ascending) |
|---------------------|------|--------------------|
| 9 4 | 10 | 3 5 |
| 7 3 3 | 21 | 0 5 7 9 |
| 9 6 5 | 50 | 2 4 |
| 7 2 | 76 | 1 5 |

Check:
- Stem 10:
B: 104, 109 → leaves: 4, 9 → descending: 9, 4
A: 103, 105 → leaves: 3, 5 → ascending: 3, 5 ✔

- Stem 21:
B: 213, 213, 217 → leaves: 3, 3, 7 → descending: 7, 3, 3
A: 210, 215, 217, 219 → leaves: 0, 5, 7, 9 → ascending: 0, 5, 7, 9 ✔

- Stem 50:
B: 505, 506, 509 → leaves: 5, 6, 9 → descending: 9, 6, 5
A: 502, 504 → leaves: 2, 4 → ascending: 2, 4 ✔

- Stem 76:
B: 762, 767 → leaves: 2, 7 → descending: 7, 2
A: 761, 765 → leaves: 1, 5 → ascending: 1, 5 ✔

Key: `10|3 = ___`

This means: stem 10, leaf 3 → number is 103

So:
Key: 10|3 = 103

✔ Final Answer for Problem 2:

```
Leaf B | Stem | Leaf A
------------|------|--------
9 4 | 10 | 3 5
7 3 3 | 21 | 0 5 7 9
9 6 5 | 50 | 2 4
7 2 | 76 | 1 5
```

Key: 10|3 = 103

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✔ Final Answers:

#### Problem 1:

```
Leaf B | Stem | Leaf A
------------|------|--------
7 6 3 1 | 2 | 0 5 9
9 2 | 3 | 1 8
7 | 6 | 6 7
8 2 0 | 8 | 3 4 6
```

Key: 3|8 = 38

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#### Problem 2:

```
Leaf B | Stem | Leaf A
------------|------|--------
9 4 | 10 | 3 5
7 3 3 | 21 | 0 5 7 9
9 6 5 | 50 | 2 4
7 2 | 76 | 1 5
```

Key: 10|3 = 103

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