Worksheet for creating box plots from given data sets on a number line.

Let’s solve both problems step by step, calculating the five-number summary (Minimum, Q1, Median, Q3, Maximum) and then the Range and Interquartile Range (IQR) for each.

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## 🔹 PROBLEM 1: Geography Test Marks

Data:
13, 12, 9, 11, 14, 12, 10, 15, 11, 10, 7

Step 1: Sort the data in ascending order

7, 9, 10, 10, 11, 11, 12, 12, 13, 14, 15

→ There are 11 values (odd number)

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Step 2: Find the Minimum and Maximum

- Minimum value = 7
- Maximum value = 15

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Step 3: Find the Median (Q2)

Median is the middle value → position = (n+1)/2 = (11+1)/2 = 6th value

Sorted list:
1st: 7
2nd: 9
3rd: 10
4th: 10
5th: 11
6th: 11 ← Median
7th: 12
8th: 12
9th: 13
10th: 14
11th: 15

→ Median = 11

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Step 4: Find the 1st Quartile (Q1)

Q1 is the median of the lower half (excluding the overall median if n is odd).

Lower half (first 5 numbers): 7, 9, 10, 10, 11

→ Median of these 5 = 3rd value = 10

→ Q1 = 10

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Step 5: Find the 3rd Quartile (Q3)

Q3 is the median of the upper half (excluding the overall median).

Upper half (last 5 numbers): 12, 12, 13, 14, 15

→ Median of these 5 = 3rd value = 13

→ Q3 = 13

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Step 6: Calculate Range and IQR

- Range = Max - Min = 15 - 7 = 8
- Interquartile Range (IQR) = Q3 - Q1 = 13 - 10 = 3

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✔ Answer for Problem 1:

| Minimum value | 1st quartile | Median | 3rd quartile | Maximum value | Range | Interquartile Range |
|---------------|--------------|--------|--------------|---------------|-------|---------------------|
| 7 | 10 | 11 | 13 | 15 | 8 | 3 |

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## 🔹 PROBLEM 2: Number of Visitors to Art Gallery

Data:
25, 17, 32, 22, 19, 20, 25, 31, 24, 20

Step 1: Sort the data in ascending order

17, 19, 20, 20, 22, 24, 25, 25, 31, 32

→ There are 10 values (even number)

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Step 2: Find Minimum and Maximum

- Minimum value = 17
- Maximum value = 32

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Step 3: Find the Median (Q2)

Median = average of 5th and 6th values (since n=10, even)

Sorted list:
1st: 17
2nd: 19
3rd: 20
4th: 20
5th: 22
6th: 24
7th: 25
8th: 25
9th: 31
10th: 32

→ Median = (22 + 24)/2 = 23

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Step 4: Find the 1st Quartile (Q1)

Q1 = median of the first half (first 5 numbers): 17, 19, 20, 20, 22

→ Median of these 5 = 3rd value = 20

→ Q1 = 20

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Step 5: Find the 3rd Quartile (Q3)

Q3 = median of the second half (last 5 numbers): 24, 25, 25, 31, 32

→ Median of these 5 = 3rd value = 25

→ Q3 = 25

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Step 6: Calculate Range and IQR

- Range = Max - Min = 32 - 17 = 15
- Interquartile Range (IQR) = Q3 - Q1 = 25 - 20 = 5

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✔ Answer for Problem 2:

| Minimum value | 1st quartile | Median | 3rd quartile | Maximum value | Range | Interquartile Range |
|---------------|--------------|--------|--------------|---------------|-------|---------------------|
| 17 | 20 | 23 | 25 | 32 | 15 | 5 |

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## 📊 How to Draw the Box Plots (Brief Instructions):

For each problem:

1. Draw a number line with appropriate scale (already provided on worksheet).
2. Mark the 5-number summary points: Min, Q1, Median, Q3, Max.
3. Draw a box from Q1 to Q3.
4. Draw a vertical line inside the box at the Median.
5. Draw “whiskers” from the box to Min and Max.

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✔ Final Answers Filled In:

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Problem 1 Table:

| Minimum value | 1st quartile | Median | 3rd quartile | Maximum value | Range | Interquartile Range |
|---------------|--------------|--------|--------------|---------------|-------|---------------------|
| 7 | 10 | 11 | 13 | 15 | 8 | 3 |

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Problem 2 Table:

| Minimum value | 1st quartile | Median | 3rd quartile | Maximum value | Range | Interquartile Range |
|---------------|--------------|--------|--------------|---------------|-------|---------------------|
| 17 | 20 | 23 | 25 | 32 | 15 | 5 |

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Let me know if you’d like help drawing the actual box plots visually!