Practice worksheet for creating box plots using number sets and number lines.

Let's solve each of the three box plot problems step by step. We'll follow the instructions:

Step 1: Find 5-number summary (minimum, Q1, median, Q3, maximum).
Step 2: Draw a number line labeled with an appropriate scale.
Step 3: Draw a box plot above the number line.

We’ll compute the five-number summary for each data set.

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Problem (i): 11, 7, 18, 14, 19, 21, 12, 5, 2

#### Step 1: Order the data
First, sort the numbers in ascending order:
2, 5, 7, 11, 12, 14, 18, 19, 21

Now find the five-number summary:

- Min = smallest value = 2
- Max = largest value = 21

There are 9 numbers (odd), so:
- Median = middle value = 5th number = 12

Now find Q1 (first quartile) and Q3 (third quartile).

- Q1: Median of the lower half (not including median if odd)
- Lower half: 2, 5, 7, 11 → 4 numbers
- Median of these = average of 2nd and 3rd: (5 + 7)/2 = 6
- Q3: Median of the upper half: 14, 18, 19, 21 → (18 + 19)/2 = 18.5

So:
- Min = 2
- Q1 = 6
- Median = 12
- Q3 = 18.5
- Max = 21

✔ Fill in the blanks:
```
Min = 2
Q1 = 6
Median = 12
Q3 = 18.5
Max = 21
```

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Problem (ii): 10, 5, 20, 12, 4, 25, 29, 25, 30

#### Step 1: Order the data
Sort: 4, 5, 10, 12, 20, 25, 25, 29, 30

- Min = 4
- Max = 30

Number of values: 9 → odd → median is the 5th value = 20

Now find Q1 and Q3:

- Q1: Lower half: 4, 5, 10, 12 → median = (5 + 10)/2 = 7.5
- Q3: Upper half: 25, 25, 29, 30 → median = (25 + 29)/2 = 27

So:
- Min = 4
- Q1 = 7.5
- Median = 20
- Q3 = 27
- Max = 30

✔ Fill in the blanks:
```
Min = 4
Q1 = 7.5
Median = 20
Q3 = 27
Max = 30
```

---

Problem (iii): 76, 71, 73, 66, 75, 72, 62, 77

#### Step 1: Order the data
Sort: 62, 66, 71, 72, 73, 75, 76, 77

- Min = 62
- Max = 77

Number of values: 8 → even → median = average of 4th and 5th values:
- (72 + 73)/2 = 72.5

Now find Q1 and Q3:

- Q1: Lower half: 62, 66, 71, 72 → median = (66 + 71)/2 = 68.5
- Q3: Upper half: 73, 75, 76, 77 → median = (75 + 76)/2 = 75.5

So:
- Min = 62
- Q1 = 68.5
- Median = 72.5
- Q3 = 75.5
- Max = 77

✔ Fill in the blanks:
```
Min = 62
Q1 = 68.5
Median = 72.5
Q3 = 75.5
Max = 77
```

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Summary of Answers:

(i)
Min = 2
Q1 = 6
Median = 12
Q3 = 18.5
Max = 21

(ii)
Min = 4
Q1 = 7.5
Median = 20
Q3 = 27
Max = 30

(iii)
Min = 62
Q1 = 68.5
Median = 72.5
Q3 = 75.5
Max = 77

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Step 2 & 3: Drawing the Box Plots

For each problem:

1. Draw a number line that spans from min to max.
- For (i): 0 to 25 (or 0–22)
- For (ii): 0 to 35
- For (iii): 60 to 80
2. Mark the five-number summary points on the line.
3. Draw a box from Q1 to Q3, with a line at the median.
4. Draw "whiskers" from Q1 to min and Q3 to max.

> Since I can't draw here, you can sketch it using the values above.

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✔ Final Answer:

| Problem | Min | Q1 | Median | Q3 | Max |
|--------|-----|----|--------|----|-----|
| (i) | 2 | 6 | 12 | 18.5 | 21 |
| (ii) | 4 | 7.5| 20 | 27 | 30 |
| (iii) | 62 | 68.5| 72.5 | 75.5 | 77 |

You now have all the values needed to create accurate box plots!