Drawing Bar Graphs from Frequency Tables (B) Worksheet | Fun and ... - Free Printable

Let's solve both problems step by step.

---

Problem 1: Car Colors

We are given a list of the colors of 20 cars sold by a car dealer:

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

#### a. Complete the frequency table

We need to count how many times each color appears.

- Black:
Count: Black, Black, Black, Black, Black → 5 times
Tally: ||||| (or five vertical lines)

- Red:
Count: Red, Red, Red, Red, Red, Red, Red, Red, Red, Red → 10 times
Tally: |||| |||| ||

- White:
Count: White, White, White, White → 4 times
Tally: ||||

- Silver:
Count: Silver, Silver → 2 times
Tally: ||

Now fill in the table:

| Colour | Tally | Frequency |
|---------|-------------|-----------|
| Black | ||||| | 5 |
| Red | |||| |||| ||| | 10 |
| White | |||| | 4 |
| Silver | || | 2 |

> ✔ Total: 5 + 10 + 4 + 2 = 21? Wait — that’s 21! But we only have 20 cars.

Let’s double-check the original list.

List:
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 again:

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

Wait — let's go through one more time carefully.

List with numbers:

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 tally:

- Black: 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 ✔

So correct frequencies:

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

Tally marks:
- Black: 6 → ||||| |
- Red: 8 → |||| ||||
- White: 4 → ||||
- Silver: 2 → ||

✔ Now corrected.

---

#### b. Draw a bar chart

To draw a bar chart:

- X-axis: Color (Black, Red, White, Silver)
- Y-axis: Frequency (number of cars), scale from 0 to 8 or 10
- Bars should be of equal width, spaced evenly
- Height of each bar corresponds to frequency

Example sketch:

```
Frequency
8 | █
7 | █
6 | █ █
5 | █ █
4 | █ █ █
3 | █ █ █
2 | █ █ █ █
1 | █ █ █ █
0 +---------------------------------
Black Red White Silver
```

But since this is text, just describe:

- Bar for Black: height 6
- Bar for Red: height 8
- Bar for White: height 4
- Bar for Silver: height 2

Label axes: "Colour" on x-axis, "Frequency" on y-axis.

---

Problem 2: Heights of Students

Given heights (in meters):

```
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
```

Grouped intervals:

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

Go through each value and assign it to a group.

---

#### Step-by-step grouping:

1. 1.51 → 1.50–1.59 ✔
2. 1.50 → 1.50–1.59 ✔
3. 1.82 → 1.80–1.89 ✔
4. 1.63 → 1.60–1.69 ✔
5. 1.75 → 1.70–1.79 ✔
6. 1.58 → 1.50–1.59 ✔
7. 1.66 → 1.60–1.69 ✔
8. 1.92 → 1.90–1.99 ✔
9. 1.64 → 1.60–1.69 ✔
10. 1.81 → 1.80–1.89 ✔
11. 1.74 → 1.70–1.79 ✔
12. 1.59 → 1.50–1.59 ✔
13. 1.63 → 1.60–1.69 ✔
14. 1.68 → 1.60–1.69 ✔
15. 1.70 → 1.70–1.79 ✔
16. 1.49 → 1.40–1.49 ✔
17. 1.75 → 1.70–1.79 ✔
18. 1.52 → 1.50–1.59 ✔
19. 1.63 → 1.60–1.69 ✔
20. 1.60 → 1.60–1.69 ✔

Now count per group:

- 1.40–1.49: only 1.49 → 1
- 1.50–1.59: 1.51, 1.50, 1.58, 1.59, 1.52 → 5
- 1.60–1.69: 1.63, 1.66, 1.64, 1.63, 1.68, 1.63, 1.60 → 7
- 1.70–1.79: 1.75, 1.74, 1.70, 1.75 → 4
- 1.80–1.89: 1.82, 1.81 → 2
- 1.90–1.99: 1.92 → 1

Check total: 1 + 5 + 7 + 4 + 2 + 1 = 20 ✔

Now fill in the 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 |

---

#### b. Draw a bar chart

- X-axis: Height ranges (e.g., 1.40–1.49, etc.)
- Y-axis: Frequency (0 to 7)
- Each bar represents one group
- Heights:
- 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

Label axes: "Height (m)" on x-axis, "Frequency" on y-axis.

Bar heights:
- 1.40–1.49: 1 unit
- 1.50–1.59: 5 units
- 1.60–1.69: 7 units (tallest)
- 1.70–1.79: 4 units
- 1.80–1.89: 2 units
- 1.90–1.99: 1 unit

---

✔ Final Answers

---

Problem 1: Car Colors

#### a. Completed Frequency Table:

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

#### b. Bar Chart Instructions:
- Draw bars with heights: Black=6, Red=8, White=4, Silver=2
- Label x-axis: “Colour”, y-axis: “Frequency”

---

Problem 2: Student Heights

#### a. 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 |

#### b. Bar Chart Instructions:
- Draw bars with heights: 1, 5, 7, 4, 2, 1 respectively
- Label x-axis: “Height (m)”, y-axis: “Frequency”
- Use consistent width and spacing

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Let me know if you'd like a visual sketch of the bar charts (as ASCII art).