Box Plot Worksheets - Free Printable

Let’s solve each part step by step.

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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 order from smallest to largest.

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

There are 11 numbers.

Step 2: Find the Minimum value → smallest number = 7

Step 3: Find the Maximum value → largest number = 15

Step 4: Find the Median (middle value). Since there are 11 numbers, the median is the 6th number.

Count:
1st: 7
2nd: 9
3rd: 10
4th: 10
5th: 11
→ 6th: 11 ← Median

So, Median = 11

Step 5: Find the 1st quartile (Q1) — this is the median of the lower half (not including the overall median if odd count).

Lower half (first 5 numbers): 7, 9, 10, 10, 11
Median of these 5 → 3rd number = 10

So, Q1 = 10

Step 6: Find the 3rd quartile (Q3) — median of the upper half (after the median).

Upper half (last 5 numbers): 12, 12, 13, 14, 15
Median of these 5 → 3rd number = 13

So, Q3 = 13

Step 7: Range = Maximum - Minimum = 15 - 7 = 8

Step 8: Interquartile Range (IQR) = Q3 - Q1 = 13 - 10 = 3

✔ Final values for Problem 1:

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

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Problem 2: Art Gallery Visitors

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

Step 1: Sort the data.

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

There are 10 numbers (even).

Step 2: Minimum = 17
Maximum = 32

Step 3: Median — average of the two middle numbers (5th and 6th)

5th: 22
6th: 24
Median = (22 + 24) / 2 = 23

Step 4: 1st quartile (Q1) — median of the first half (first 5 numbers)

First half: 17, 19, 20, 20, 22
Median of these 5 → 3rd number = 20

So, Q1 = 20

Step 5: 3rd quartile (Q3) — median of the second half (last 5 numbers)

Second half: 24, 25, 25, 31, 32
Median of these 5 → 3rd number = 25

So, Q3 = 25

Step 6: Range = 32 - 17 = 15

Step 7: Interquartile Range (IQR) = 25 - 20 = 5

✔ Final values for Problem 2:

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

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Final Answer:

Problem 1:
Minimum: 7
1st quartile: 10
Median: 11
3rd quartile: 13
Maximum: 15
Range: 8
Interquartile Range: 3

Problem 2:
Minimum: 17
1st quartile: 20
Median: 23
3rd quartile: 25
Maximum: 32
Range: 15
Interquartile Range: 5