Cumulative Frequency Graphs - Go Teach Maths: Handcrafted ... - Free Printable

Let’s solve both problems step by step.

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## Problem 1: Car Colors

We are given a list of 20 car colors sold. We need to:

a. Complete the frequency table (with tally and frequency).
b. Draw a bar chart (we’ll describe how to draw it since we can’t draw here).

Step 1: Count each color

List of 20 cars:

```
Black, Red, White, Silver, Red
Red, Red, White, Black, Red
Red, White, Silver, Black, Red
Red, Black, Black, Black, White
```

Let’s count each color:

- Black: Let’s find all “Black”:
- Row 1: 1
- Row 2: 1 (5th)
- Row 3: 1 (4th), 1 (5th) → total 2 in row 3
- Row 4: 1 (2nd), 1 (3rd), 1 (4th), 1 (5th) → 4 in row 4
- Total Black = 1 + 1 + 2 + 4 = 8

- Red:
- Row 1: 2 (positions 2 and 5)
- Row 2: 4 (positions 1,2,4,5)
- Row 3: 3 (positions 1,4,5)
- Row 4: 1 (position 1)
- Total Red = 2 + 4 + 3 + 1 = 10

Wait — that’s already 18. Let’s recount carefully.

Better way: Go one by one.

Full list (numbered for clarity):

1. Black
2. Red
3. White
4. Silver
5. Red
6. Red
7. Red
8. White
9. Black
10. Red
11. Red
12. White
13. Silver
14. Black
15. Red
16. Red
17. Black
18. Black
19. Black
20. White

Now count:

- Black: positions 1, 9, 14, 17, 18, 19 → 6
- Red: 2,5,6,7,10,11,15,16 → 8
- White: 3,8,12,20 → 4
- Silver: 4,13 → 2

✔ Total: 6 + 8 + 4 + 2 = 20 ✔️

Step 2: Fill the frequency table

| Colour | Tally | Frequency |
|--------|--------------|---------|
| Black | |||| || | 6 |
| Red | |||| |||| | 8 |
| White | |||| | 4 |
| Silver | || | 2 |

*(Tally marks: Each "|" is 1, group of 5 is "||||" with diagonal line, but here we just use straight lines for simplicity.)*

Step 3: Draw the bar chart

- X-axis: Car colors — Black, Red, White, Silver (in order)
- Y-axis: Frequency (from 0 to at least 8)
- Draw bars with heights:
- Black: 6 units high
- Red: 8 units high
- White: 4 units high
- Silver: 2 units high

Label axes and give a title like “Car Colors Sold”.

---

## Problem 2: Student Heights

We have 20 height measurements (in meters). We need to:

a. Complete the grouped frequency table.
b. Draw a bar chart.

Step 1: List of heights

Given:

```
1.51 1.50 1.82 1.63 1.75
1.58 1.66 1.92 1.64 1.81
1.74 1.59 1.63 1.68 1.70
1.49 1.75 1.52 1.63 1.60
```

Groupings:

- 1.40 - 1.49
- 1.50 - 1.59
- 1.60 - 1.69
- 1.70 - 1.79
- 1.80 - 1.89
- 1.90 - 1.99

Step 2: Sort and assign to groups

Go through each value:

- 1.40 - 1.49: Only 1.49 → count = 1
- 1.50 - 1.59:
- 1.51, 1.50, 1.58, 1.59, 1.52 → that’s 5 values
- 1.60 - 1.69:
- 1.63, 1.66, 1.64, 1.63, 1.68, 1.63, 1.60 → 7 values
- 1.70 - 1.79:
- 1.75, 1.74, 1.70, 1.75 → 4 values
- 1.80 - 1.89:
- 1.82, 1.81 → 2 values
- 1.90 - 1.99:
- 1.92 → 1 value

✔ Total: 1 + 5 + 7 + 4 + 2 + 1 = 20 ✔️

Step 3: Fill the grouped frequency table

| Height (m) | Tally | Frequency |
|----------------|----------------|---------|
| 1.40 - 1.49 | | | 1 |
| 1.50 - 1.59 | |||| | 5 |
| 1.60 - 1.69 | |||| || | 7 |
| 1.70 - 1.79 | |||| | 4 |
| 1.80 - 1.89 | || | 2 |
| 1.90 - 1.99 | | | 1 |

*(Tally: Use “|” for each, group 5s as “||||” if needed.)*

Step 4: Draw the bar chart

- X-axis: Height intervals (1.40–1.49, 1.50–1.59, etc.)
- Y-axis: Frequency (0 to at least 7)
- Bars:
- 1.40–1.49: height 1
- 1.50–1.59: height 5
- 1.60–1.69: height 7
- 1.70–1.79: height 4
- 1.80–1.89: height 2
- 1.90–1.99: height 1

Label axes: X = “Height (m)”, Y = “Frequency”. Title: “Heights of Year 11 Students”.

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## ✔ Final Answers:

Problem 1 Table:

| Colour | Tally | Frequency |
|--------|--------------|---------|
| Black | |||| || | 6 |
| Red | |||| |||| | 8 |
| White | |||| | 4 |
| Silver | || | 2 |

Bar chart: Bars for Black=6, Red=8, White=4, Silver=2.

---

Problem 2 Table:

| Height (m) | Tally | Frequency |
|----------------|----------------|---------|
| 1.40 - 1.49 | | | 1 |
| 1.50 - 1.59 | |||| | 5 |
| 1.60 - 1.69 | |||| || | 7 |
| 1.70 - 1.79 | |||| | 4 |
| 1.80 - 1.89 | || | 2 |
| 1.90 - 1.99 | | | 1 |

Bar chart: Bars for each interval with heights 1,5,7,4,2,1 respectively.

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You can now draw the bar charts on the grids provided using these frequencies!