Math worksheet focusing on stem and leaf plots, featuring two data sets for creating plots and questions about a sample plot of test scores.
A worksheet titled "STEM AND LEAF PLOTS practice" with two problems involving creating stem and leaf plots from given data sets, followed by questions about a provided stem and leaf plot of test scores.
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Step-by-step solution for: Stem and Leaf Plots Notes and Worksheets - Lindsay Bowden
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Show Answer Key & Explanations
Step-by-step solution for: Stem and Leaf Plots Notes and Worksheets - Lindsay Bowden
Let's solve each part of this Stem and Leaf Plot Practice worksheet step by step.
---
Data:
27, 45, 56, 31, 29, 36, 42, 50, 43, 61, 59, 48, 36, 23
#### Step 1: Sort the data
Sorted:
23, 27, 29, 31, 36, 36, 42, 43, 45, 48, 50, 56, 59, 61
#### Step 2: Create a stem-and-leaf plot
- Stem = tens digit
- Leaf = ones digit
| Stem | Leaf |
|------|------|
| 2 | 3, 7, 9 |
| 3 | 1, 6, 6 |
| 4 | 2, 3, 5, 8 |
| 5 | 0, 6, 9 |
| 6 | 1 |
> Note: The leaf values are listed in ascending order.
---
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
This data has decimal values. For a stem-and-leaf plot, we can use:
- Stem = whole number part
- Leaf = tenths digit (multiply by 10 to make it easier)
But since decimals are involved, we can treat them as if they were integers by multiplying all values by 10 (i.e., work with tenths):
Convert data to tenths:
35, 48, 21, 56, 43, 39, 60, 59, 27, 49, 58, 35
Now sort:
21, 27, 35, 35, 39, 43, 48, 49, 56, 58, 59, 60
Now create stem-and-leaf plot:
| Stem | Leaf |
|------|------|
| 2 | 1, 7 |
| 3 | 5, 5, 9 |
| 4 | 3, 8, 9 |
| 5 | 6, 8, 9 |
| 6 | 0 |
> Note: Each stem represents the whole number (e.g., "2" means 2.x), and leaves represent tenths.
To interpret:
- 2 | 1 → 2.1 ft
- 3 | 5 → 3.5 ft
- etc.
So final stem-and-leaf plot for jump distances:
| Stem | Leaf |
|------|------|
| 2 | 1, 7 |
| 3 | 5, 5, 9 |
| 4 | 3, 8, 9 |
| 5 | 6, 8, 9 |
| 6 | 0 |
---
The plot shows test scores:
```
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
```
We'll now answer questions based on this.
---
#### Step 1: List all the scores from the plot
Each score is: `stem + leaf` (e.g., 7 | 1 → 71)
List of scores:
- 35
- 55
- 66, 68
- 71, 73, 74, 78, 78, 78, 79
- 80, 82, 86, 86
- 91, 93, 94, 99
- 100, 100
Now write them in order:
35, 55, 66, 68, 71, 73, 74, 78, 78, 78, 79, 80, 82, 86, 86, 91, 93, 94, 99, 100, 100
Count: Let's count how many scores there are.
- 35 → 1
- 55 → 1
- 66,68 → 2
- 71,73,74,78,78,78,79 → 7
- 80,82,86,86 → 4
- 91,93,94,99 → 4
- 100,100 → 2
Total: 1+1+2+7+4+4+2 = 21 scores
---
Sum all scores:
Break it down:
- 35
- 55
- 66 + 68 = 134
- 71 + 73 + 74 + 78×3 + 79 = 71+73=144; 144+74=218; 218+234=452; 452+79=531
- 80 + 82 + 86 + 86 = 80+82=162; 162+172=334
- 91 + 93 + 94 + 99 = 91+93=184; 184+94=278; 278+99=377
- 100 + 100 = 200
Now sum all:
35 + 55 = 90
90 + 134 = 224
224 + 531 = 755
755 + 334 = 1089
1089 + 377 = 1466
1466 + 200 = 1666
Total sum = 1666
Number of scores = 21
Mean = 1666 ÷ 21 ≈ 79.33
✔ Answer: 79.33 (or about 79.3)
---
Mode = most frequent value
Look at frequencies:
- 35 → 1
- 55 → 1
- 66 → 1, 68 → 1
- 71 → 1, 73 → 1, 74 → 1, 78 → 3, 79 → 1
- 80 → 1, 82 → 1, 86 → 2
- 91 → 1, 93 → 1, 94 → 1, 99 → 1
- 100 → 2
Most frequent: 78 appears 3 times
✔ Answer: Yes, the mode is 78
---
Outliers are values significantly different from others.
Look at spread:
Lowest: 35
Highest: 100
Most scores are between 70–100
But 35 and 55 are much lower than others.
Check interquartile range (IQR) method:
First, find Q1, Q2 (median), Q3
We have 21 scores → median is the 11th score.
Ordered list:
1. 35
2. 55
3. 66
4. 68
5. 71
6. 73
7. 74
8. 78
9. 78
10. 78
11. 79 ← median (Q2)
12. 80
13. 82
14. 86
15. 86
16. 91
17. 93
18. 94
19. 99
20. 100
21. 100
So Median = 79
Now Q1 = median of first half (first 10 scores):
Scores 1–10: 35, 55, 66, 68, 71, 73, 74, 78, 78, 78
Median of these: average of 5th and 6th → (71 + 73)/2 = 72
Q3 = median of second half (last 10 scores):
Scores 12–21: 80, 82, 86, 86, 91, 93, 94, 99, 100, 100
Median: average of 5th and 6th → (91 + 93)/2 = 92
Now IQR = Q3 - Q1 = 92 - 72 = 20
Lower fence = Q1 - 1.5×IQR = 72 - 30 = 42
Upper fence = Q3 + 1.5×IQR = 92 + 30 = 122
Any value < 42 or > 122 is an outlier.
- 35 < 42 → outlier
- 55 > 42 → not outlier
- All others are within 42–122
✔ Answer: Yes, 35 is an outlier
---
Passing = 70 or above
From the list:
All scores from 71 upward:
- 71, 73, 74, 78, 78, 78, 79 → 7 scores
- 80, 82, 86, 86 → 4
- 91, 93, 94, 99 → 4
- 100, 100 → 2
Total passing = 7 + 4 + 4 + 2 = 17
Total students = 21
Percentage = (17 / 21) × 100 ≈ 80.95%
✔ Answer: Approximately 81%
---
Range = Max - Min = 100 - 35 = 65
✔ Answer: 65
---
As found earlier: 11th score in ordered list is 79
✔ Answer: 79
---
Count per stem:
- 3 → 1 (35)
- 4 → 0
- 5 → 1 (55)
- 6 → 2 (66,68)
- 7 → 7 (71,73,74,78,78,78,79)
- 8 → 4 (80,82,86,86)
- 9 → 4 (91,93,94,99)
- 10 → 2 (100,100)
✔ Answer: Stem 7 has the highest frequency (7 scores)
---
No — the distribution is skewed.
- Most scores cluster around 70s and 80s.
- A few low scores (35, 55) and high scores (100).
- There’s a peak at 78 and then tapering off.
Also, the presence of an outlier (35) pulls the left side.
✔ Answer: No, the scores are not evenly distributed. They are skewed right (with a low outlier).
---
1. Stem-and-Leaf Plot (Teacher Ages):
| Stem | Leaf |
|------|------|
| 2 | 3, 7, 9 |
| 3 | 1, 6, 6 |
| 4 | 2, 3, 5, 8 |
| 5 | 0, 6, 9 |
| 6 | 1 |
2. Stem-and-Leaf Plot (Jump Distances):
| Stem | Leaf |
|------|------|
| 2 | 1, 7 |
| 3 | 5, 5, 9 |
| 4 | 3, 8, 9 |
| 5 | 6, 8, 9 |
| 6 | 0 |
3. Mean of scores: 79.33
4. Mode: Yes, 78
5. Outlier: Yes, 35
6. Percentage passing (70+): ~81%
7. Range: 65
8. Median score: 79
9. Highest frequency stem: 7
10. Evenly distributed? No
---
Let me know if you'd like a visual version of the plots!
---
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
Sorted:
23, 27, 29, 31, 36, 36, 42, 43, 45, 48, 50, 56, 59, 61
#### Step 2: Create a stem-and-leaf plot
- Stem = tens digit
- Leaf = ones digit
| Stem | Leaf |
|------|------|
| 2 | 3, 7, 9 |
| 3 | 1, 6, 6 |
| 4 | 2, 3, 5, 8 |
| 5 | 0, 6, 9 |
| 6 | 1 |
> Note: The leaf values are listed in ascending order.
---
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
This data has decimal values. For a stem-and-leaf plot, we can use:
- Stem = whole number part
- Leaf = tenths digit (multiply by 10 to make it easier)
But since decimals are involved, we can treat them as if they were integers by multiplying all values by 10 (i.e., work with tenths):
Convert data to tenths:
35, 48, 21, 56, 43, 39, 60, 59, 27, 49, 58, 35
Now sort:
21, 27, 35, 35, 39, 43, 48, 49, 56, 58, 59, 60
Now create stem-and-leaf plot:
| Stem | Leaf |
|------|------|
| 2 | 1, 7 |
| 3 | 5, 5, 9 |
| 4 | 3, 8, 9 |
| 5 | 6, 8, 9 |
| 6 | 0 |
> Note: Each stem represents the whole number (e.g., "2" means 2.x), and leaves represent tenths.
To interpret:
- 2 | 1 → 2.1 ft
- 3 | 5 → 3.5 ft
- etc.
So final stem-and-leaf plot for jump distances:
| Stem | Leaf |
|------|------|
| 2 | 1, 7 |
| 3 | 5, 5, 9 |
| 4 | 3, 8, 9 |
| 5 | 6, 8, 9 |
| 6 | 0 |
---
Problems 3–10: Using the Given Stem-and-Leaf Plot
The plot shows test scores:
```
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
```
We'll now answer questions based on this.
---
#### Step 1: List all the scores from the plot
Each score is: `stem + leaf` (e.g., 7 | 1 → 71)
List of scores:
- 35
- 55
- 66, 68
- 71, 73, 74, 78, 78, 78, 79
- 80, 82, 86, 86
- 91, 93, 94, 99
- 100, 100
Now write them in order:
35, 55, 66, 68, 71, 73, 74, 78, 78, 78, 79, 80, 82, 86, 86, 91, 93, 94, 99, 100, 100
Count: Let's count how many scores there are.
- 35 → 1
- 55 → 1
- 66,68 → 2
- 71,73,74,78,78,78,79 → 7
- 80,82,86,86 → 4
- 91,93,94,99 → 4
- 100,100 → 2
Total: 1+1+2+7+4+4+2 = 21 scores
---
Question 3: What is the mean of the scores?
Sum all scores:
Break it down:
- 35
- 55
- 66 + 68 = 134
- 71 + 73 + 74 + 78×3 + 79 = 71+73=144; 144+74=218; 218+234=452; 452+79=531
- 80 + 82 + 86 + 86 = 80+82=162; 162+172=334
- 91 + 93 + 94 + 99 = 91+93=184; 184+94=278; 278+99=377
- 100 + 100 = 200
Now sum all:
35 + 55 = 90
90 + 134 = 224
224 + 531 = 755
755 + 334 = 1089
1089 + 377 = 1466
1466 + 200 = 1666
Total sum = 1666
Number of scores = 21
Mean = 1666 ÷ 21 ≈ 79.33
✔ Answer: 79.33 (or about 79.3)
---
Question 4: Is there a mode? If so, what is it?
Mode = most frequent value
Look at frequencies:
- 35 → 1
- 55 → 1
- 66 → 1, 68 → 1
- 71 → 1, 73 → 1, 74 → 1, 78 → 3, 79 → 1
- 80 → 1, 82 → 1, 86 → 2
- 91 → 1, 93 → 1, 94 → 1, 99 → 1
- 100 → 2
Most frequent: 78 appears 3 times
✔ Answer: Yes, the mode is 78
---
Question 5: Is there an outlier?
Outliers are values significantly different from others.
Look at spread:
Lowest: 35
Highest: 100
Most scores are between 70–100
But 35 and 55 are much lower than others.
Check interquartile range (IQR) method:
First, find Q1, Q2 (median), Q3
We have 21 scores → median is the 11th score.
Ordered list:
1. 35
2. 55
3. 66
4. 68
5. 71
6. 73
7. 74
8. 78
9. 78
10. 78
11. 79 ← median (Q2)
12. 80
13. 82
14. 86
15. 86
16. 91
17. 93
18. 94
19. 99
20. 100
21. 100
So Median = 79
Now Q1 = median of first half (first 10 scores):
Scores 1–10: 35, 55, 66, 68, 71, 73, 74, 78, 78, 78
Median of these: average of 5th and 6th → (71 + 73)/2 = 72
Q3 = median of second half (last 10 scores):
Scores 12–21: 80, 82, 86, 86, 91, 93, 94, 99, 100, 100
Median: average of 5th and 6th → (91 + 93)/2 = 92
Now IQR = Q3 - Q1 = 92 - 72 = 20
Lower fence = Q1 - 1.5×IQR = 72 - 30 = 42
Upper fence = Q3 + 1.5×IQR = 92 + 30 = 122
Any value < 42 or > 122 is an outlier.
- 35 < 42 → outlier
- 55 > 42 → not outlier
- All others are within 42–122
✔ Answer: Yes, 35 is an outlier
---
Question 6: What percentage of the class passed the test (70+)?
Passing = 70 or above
From the list:
All scores from 71 upward:
- 71, 73, 74, 78, 78, 78, 79 → 7 scores
- 80, 82, 86, 86 → 4
- 91, 93, 94, 99 → 4
- 100, 100 → 2
Total passing = 7 + 4 + 4 + 2 = 17
Total students = 21
Percentage = (17 / 21) × 100 ≈ 80.95%
✔ Answer: Approximately 81%
---
Question 7: What is the range?
Range = Max - Min = 100 - 35 = 65
✔ Answer: 65
---
Question 8: What is the median score?
As found earlier: 11th score in ordered list is 79
✔ Answer: 79
---
Question 9: Which stem has the highest frequency?
Count per stem:
- 3 → 1 (35)
- 4 → 0
- 5 → 1 (55)
- 6 → 2 (66,68)
- 7 → 7 (71,73,74,78,78,78,79)
- 8 → 4 (80,82,86,86)
- 9 → 4 (91,93,94,99)
- 10 → 2 (100,100)
✔ Answer: Stem 7 has the highest frequency (7 scores)
---
Question 10: Are the scores evenly distributed?
No — the distribution is skewed.
- Most scores cluster around 70s and 80s.
- A few low scores (35, 55) and high scores (100).
- There’s a peak at 78 and then tapering off.
Also, the presence of an outlier (35) pulls the left side.
✔ Answer: No, the scores are not evenly distributed. They are skewed right (with a low outlier).
---
✔ Final Answers Summary:
1. Stem-and-Leaf Plot (Teacher Ages):
| Stem | Leaf |
|------|------|
| 2 | 3, 7, 9 |
| 3 | 1, 6, 6 |
| 4 | 2, 3, 5, 8 |
| 5 | 0, 6, 9 |
| 6 | 1 |
2. Stem-and-Leaf Plot (Jump Distances):
| Stem | Leaf |
|------|------|
| 2 | 1, 7 |
| 3 | 5, 5, 9 |
| 4 | 3, 8, 9 |
| 5 | 6, 8, 9 |
| 6 | 0 |
3. Mean of scores: 79.33
4. Mode: Yes, 78
5. Outlier: Yes, 35
6. Percentage passing (70+): ~81%
7. Range: 65
8. Median score: 79
9. Highest frequency stem: 7
10. Evenly distributed? No
---
Let me know if you'd like a visual version of the plots!
Parent Tip: Review the logic above to help your child master the concept of stem and leaf plot worksheet 7th grade.
