Stem and Leaf Plots Notes and Worksheets - Lindsay Bowden - Free Printable

Let’s solve each problem step by step.

---

Problem 1: Ages of teachers at Drew High School

Data:
27, 45, 56, 31, 29, 36, 42, 50, 43, 61, 59, 48, 36, 23

Step 1: Sort the data (optional but helpful):
23, 27, 29, 31, 36, 36, 42, 43, 45, 48, 50, 56, 59, 61

Step 2: Break into stems and leaves.
Stem = tens digit, Leaf = ones digit.

- Stem 2 → Leaves: 3, 7, 9
- Stem 3 → Leaves: 1, 6, 6
- Stem 4 → Leaves: 2, 3, 5, 8
- Stem 5 → Leaves: 0, 6, 9
- Stem 6 → Leaves: 1

So the stem-and-leaf plot is:

```
2 | 3 7 9
3 | 1 6 6
4 | 2 3 5 8
5 | 0 6 9
6 | 1
```

*(Note: Some plots list leaves in order — we did that here.)*

---

Problem 2: Horizontal jump distances in feet

Data:
3.5, 4.8, 2.1, 5.6, 4.3, 3.9, 6.0, 5.9, 2.7, 4.9, 5.8, 3.5

Step 1: Since these are decimals, we can use the whole number as the stem and the decimal part as the leaf.

But note: 6.0 → stem 6, leaf 0
Also, 3.5 appears twice.

Sort the data to make it easier:
2.1, 2.7, 3.5, 3.5, 3.9, 4.3, 4.8, 4.9, 5.6, 5.8, 5.9, 6.0

Step 2: Create stem-and-leaf plot.

Stem = units digit, Leaf = tenths digit.

- Stem 2 → Leaves: 1, 7
- Stem 3 → Leaves: 5, 5, 9
- Stem 4 → Leaves: 3, 8, 9
- Stem 5 → Leaves: 6, 8, 9
- Stem 6 → Leaves: 0

Plot:

```
2 | 1 7
3 | 5 5 9
4 | 3 8 9
5 | 6 8 9
6 | 0
```

---

Now for Questions 3–10 using Mrs. Mendes’ test scores stem-and-leaf plot:

Given plot:

```
Stem | Leaf
3 | 5
4 |
5 | 5
6 | 6, 8
7 | 1, 3, 4, 8, 8, 8, 9
8 | 0, 2, 6, 6
9 | 1, 3, 4, 9
10 | 0, 0
```

First, let’s write out all the actual scores from the plot:

- 35
- 55
- 66, 68
- 71, 73, 74, 78, 78, 78, 79
- 80, 82, 86, 86
- 91, 93, 94, 99
- 100, 100

Total number of scores: Let’s count.

Row by row:
- 3: 1 score
- 5: 1
- 6: 2
- 7: 7
- 8: 4
- 9: 4
- 10: 2

Total = 1+1+2+7+4+4+2 = 21 scores

List them in order (already sorted by stem):

35, 55, 66, 68, 71, 73, 74, 78, 78, 78, 79, 80, 82, 86, 86, 91, 93, 94, 99, 100, 100

---

Question 3: What is the mean of the scores?

Mean = sum of all scores ÷ number of scores

Let’s add them up:

Start adding:

35 + 55 = 90
90 + 66 = 156
156 + 68 = 224
224 + 71 = 295
295 + 73 = 368
368 + 74 = 442
442 + 78 = 520
520 + 78 = 598
598 + 78 = 676
676 + 79 = 755
755 + 80 = 835
835 + 82 = 917
917 + 86 = 1003
1003 + 86 = 1089
1089 + 91 = 1180
1180 + 93 = 1273
1273 + 94 = 1367
1367 + 99 = 1466
1466 + 100 = 1566
1566 + 100 = 1666

Sum = 1666
Number of scores = 21

Mean = 1666 ÷ 21 ≈ ?

Let’s divide:

21 × 79 = 1659
1666 - 1659 = 7 → so 79 + 7/21 = 79 + 1/3 ≈ 79.33

We’ll keep it as a fraction or round to two decimals: 79.33

---

Question 4: Is there a mode? If so, what is it?

Mode = most frequent value.

Look at the list:

78 appears three times → more than any other.

Others: 86 appears twice, 100 appears twice, rest once.

So yes, mode = 78

---

Question 5: Is there an outlier?

Outlier = a value that is much higher or lower than the rest.

Lowest score: 35
Next lowest: 55 → big gap!

Then 66, 68... then 71+.

35 is 20 points below 55 — that’s a big drop.

In many classes, if a score is way below the rest, it’s considered an outlier.

Also, look at the distribution: most scores are between 70–100. Only 35 and 55 are low.

35 is especially far.

So yes, 35 is likely an outlier.

(You could also use IQR method, but since this is middle school level, visual inspection is fine.)

Answer: Yes, 35 is an outlier.

---

Question 6: What percentage of the class passed the test (70+)?

Passed = score ≥ 70

Count how many scores are 70 or above.

From our list:

Scores < 70: 35, 55, 66, 68 → 4 scores

Total scores = 21

So passed = 21 - 4 = 17

Percentage = (17 / 21) × 100

Calculate:

17 ÷ 21 ≈ 0.8095 → ×100 ≈ 80.95%

Round to nearest whole percent? Usually okay to say about 81%, but let’s be precise.

Actually, 17/21 = 1700/21 ≈ 80.952... → 81% if rounding.

But maybe they want exact fraction? The question says “percentage”, so decimal is fine.

We’ll go with 81% (rounded).

Wait — let’s double-check count:

Scores ≥70:

71,73,74,78,78,78,79 → 7
80,82,86,86 → 4
91,93,94,99 → 4
100,100 → 2

Total = 7+4+4+2 = 17 → correct.

17/21 = 0.8095 → 80.95% — perhaps leave as 81% or write 80.95%. Since it’s a math worksheet, maybe exact decimal.

But let’s see — often in such problems, they expect rounded whole number.

I’ll write 81%

---

Question 7: What is the range?

Range = highest score - lowest score

Highest = 100
Lowest = 35

Range = 100 - 35 = 65

---

Question 8: What is the median score?

Median = middle value when ordered.

We have 21 scores → odd number → median is the 11th score.

List again in order:

1: 35
2: 55
3: 66
4: 68
5: 71
6: 73
7: 74
8: 78
9: 78
10: 78
11: 79 ← median
12: 80
13: 82
14: 86
15: 86
16: 91
17: 93
18: 94
19: 99
20: 100
21: 100

So 11th score is 79

Median = 79

---

Question 9: Which stem has the highest frequency?

Frequency = number of leaves per stem.

Stem 3: 1
Stem 4: 0
Stem 5: 1
Stem 6: 2
Stem 7: 7 ← highest
Stem 8: 4
Stem 9: 4
Stem 10: 2

So stem 7 has the highest frequency (7 scores).

Answer: 7

---

Question 10: Are the scores evenly distributed?

Evenly distributed means spread out fairly equally across the range.

Looking at the plot:

Most scores are clustered in the 70s and 80s. Very few in 30s, 40s, 50s, 60s. Two 100s.

Not even — skewed toward higher scores, with a low outlier.

So answer: No

---

Final Answers:

1. Stem-and-leaf plot for teacher ages:
```
2 | 3 7 9
3 | 1 6 6
4 | 2 3 5 8
5 | 0 6 9
6 | 1
```

2. Stem-and-leaf plot for jump distances:
```
2 | 1 7
3 | 5 5 9
4 | 3 8 9
5 | 6 8 9
6 | 0
```

3. Mean = 79.33 (or approximately 79.3)

4. Mode = 78

5. Yes, 35 is an outlier.

6. 81% (or 80.95%)

7. Range = 65

8. Median = 79

9. Stem 7

10. No

──────────────────────────────────────

Final Answer:
1. Stem-and-leaf plot:
2 | 3 7 9
3 | 1 6 6
4 | 2 3 5 8
5 | 0 6 9
6 | 1

2. Stem-and-leaf plot:
2 | 1 7
3 | 5 5 9
4 | 3 8 9
5 | 6 8 9
6 | 0

3. 79.33
4. 78
5. Yes, 35
6. 81%
7. 65
8. 79
9. 7
10. No