Cumulative Frequency Diagrams (A) Worksheet | Printable Maths ... - Free Printable

You're asked to complete the cumulative frequency column in each table and then draw the cumulative frequency diagram (graph) for each.

Let’s solve this step by step.

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## 🔢 What is Cumulative Frequency?

Cumulative frequency is the running total of frequencies as you move down the table. You start with the first frequency, then add the next frequency to it, and so on.

So:
> Cumulative Frequency = Sum of all previous frequencies + current frequency

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# ✔ Problem 1: Time, t (hours)

| Time, t (hours) | Frequency | Cumulative Frequency |
|------------------|-----------|-----------------------|
| 0 < t ≤ 1 | 6 | 6 |
| 1 < t ≤ 2 | 13 | 6 + 13 = 19 |
| 2 < t ≤ 3 | 38 | 19 + 38 = 57 |
| 3 < t ≤ 4 | 34 | 57 + 34 = 91 |
| 4 < t ≤ 5 | 9 | 91 + 9 = 100 |

✔ Completed Table 1:

| Time, t (hours) | Frequency | Cumulative Frequency |
|------------------|-----------|-----------------------|
| 0 < t ≤ 1 | 6 | 6 |
| 1 < t ≤ 2 | 13 | 19 |
| 2 < t ≤ 3 | 38 | 57 |
| 3 < t ≤ 4 | 34 | 91 |
| 4 < t ≤ 5 | 9 | 100 |

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📈 How to Draw the Graph for Problem 1:

- X-axis: Time (hours) → Use the upper boundary of each class.
- So plot points at: 1, 2, 3, 4, 5
- Y-axis: Cumulative Frequency → Plot the values: 6, 19, 57, 91, 100
- Start from (0, 0) — because before time 0, cumulative frequency is 0.
- Then plot:
- (1, 6)
- (2, 19)
- (3, 57)
- (4, 91)
- (5, 100)
- Connect the points with a smooth curve or straight lines (usually straight lines for GCSE).

> 💡 Tip: The graph should start at (0,0) and end at (5,100), rising steadily.

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# ✔ Problem 2: Mass, m (kilograms)

| Mass, m (kg) | Frequency | Cumulative Frequency |
|------------------|-----------|-----------------------|
| 0 < m ≤ 10 | 19 | 19 |
| 10 < m ≤ 20 | 24 | 19 + 24 = 43 |
| 20 < m ≤ 30 | 27 | 43 + 27 = 70 |
| 30 < m ≤ 40 | 26 | 70 + 26 = 96 |
| 40 < m ≤ 50 | 4 | 96 + 4 = 100 |

✔ Completed Table 2:

| Mass, m (kg) | Frequency | Cumulative Frequency |
|------------------|-----------|-----------------------|
| 0 < m ≤ 10 | 19 | 19 |
| 10 < m ≤ 20 | 24 | 43 |
| 20 < m ≤ 30 | 27 | 70 |
| 30 < m ≤ 40 | 26 | 96 |
| 40 < m ≤ 50 | 4 | 100 |

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📈 Graph for Problem 2:

- X-axis: Mass (kg) → Upper boundaries: 10, 20, 30, 40, 50
- Y-axis: Cumulative Frequency → Values: 19, 43, 70, 96, 100
- Start at (0, 0)
- Plot:
- (10, 19)
- (20, 43)
- (30, 70)
- (40, 96)
- (50, 100)
- Connect with straight lines.

> 💡 Note: The graph ends at (50, 100) — total number of items.

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# ✔ Problem 3: Distance, d (metres)

| Distance, d (m) | Frequency | Cumulative Frequency |
|------------------|-----------|-----------------------|
| 0 < d ≤ 5 | 23 | 23 |
| 5 < d ≤ 10 | 31 | 23 + 31 = 54 |
| 10 < d ≤ 15 | 22 | 54 + 22 = 76 |
| 15 < d ≤ 20 | 3 | 76 + 3 = 79 |
| 20 < d ≤ 25 | 1 | 79 + 1 = 80 |

✔ Completed Table 3:

| Distance, d (m) | Frequency | Cumulative Frequency |
|------------------|-----------|-----------------------|
| 0 < d ≤ 5 | 23 | 23 |
| 5 < d ≤ 10 | 31 | 54 |
| 10 < d ≤ 15 | 22 | 76 |
| 15 < d ≤ 20 | 3 | 79 |
| 20 < d ≤ 25 | 1 | 80 |

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📈 Graph for Problem 3:

- X-axis: Distance (m) → Upper boundaries: 5, 10, 15, 20, 25
- Y-axis: Cumulative Frequency → Values: 23, 54, 76, 79, 80
- Start at (0, 0)
- Plot:
- (5, 23)
- (10, 54)
- (15, 76)
- (20, 79)
- (25, 80)
- Connect with straight lines.

> 💡 Notice: This graph rises quickly at first, then flattens out — meaning most data is concentrated in lower distances.

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## 🧾 Summary of Completed Tables

1) Time

| Time (h) | Freq | Cum Freq |
|-------------|------|----------|
| 0 < t ≤ 1 | 6 | 6 |
| 1 < t ≤ 2 | 13 | 19 |
| 2 < t ≤ 3 | 38 | 57 |
| 3 < t ≤ 4 | 34 | 91 |
| 4 < t ≤ 5 | 9 | 100 |

2) Mass

| Mass (kg) | Freq | Cum Freq |
|-------------|------|----------|
| 0 < m ≤ 10 | 19 | 19 |
| 10 < m ≤ 20 | 24 | 43 |
| 20 < m ≤ 30 | 27 | 70 |
| 30 < m ≤ 40 | 26 | 96 |
| 40 < m ≤ 50 | 4 | 100 |

3) Distance

| Distance (m)| Freq | Cum Freq |
|-------------|------|----------|
| 0 < d ≤ 5 | 23 | 23 |
| 5 < d ≤ 10 | 31 | 54 |
| 10 < d ≤ 15 | 22 | 76 |
| 15 < d ≤ 20 | 3 | 79 |
| 20 < d ≤ 25 | 1 | 80 |

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## 🖍️ Drawing Tips for All Graphs:

- Use a ruler to draw straight lines between points.
- Label axes clearly: “Time (hours)” / “Mass (kg)” / “Distance (m)” on x-axis; “Cumulative Frequency” on y-axis.
- Mark each point accurately using grid lines.
- Always start at (0,0).
- The final point should match the total frequency (100 for #1 & #2, 80 for #3).

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✔ You’ve now completed all tables and know how to draw the graphs!

Let me know if you’d like me to sketch the graphs for you or explain how to find median/quartiles from them next!