Box and Whisker Plots-Level1-1 | PDF - Free Printable

Let's solve each of the three problems step by step to create box-and-whisker plots (also called box plots). We'll find:

- Minimum – the smallest value
- Maximum – the largest value
- Q₁ (First Quartile) – median of the lower half
- Q₂ (Second Quartile / Median) – middle value of the entire data set
- Q₃ (Third Quartile) – median of the upper half

We’ll sort the data first, then calculate the five-number summary.

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Problem 1:

Data: 17, 29, 32, 9, 30, 14, 8, 39, 11, 32, 23

#### Step 1: Sort the data
Arrange in ascending order:
8, 9, 11, 14, 17, 23, 29, 30, 32, 32, 39

There are 11 values (odd), so:

- Minimum: 8
- Maximum: 39

#### Find Q₂ (Median):
The middle value is the 6th number:
→ Q₂ = 23

#### Find Q₁ (First Quartile):
Lower half (excluding median):
8, 9, 11, 14, 17 → 5 numbers
Middle of this half is the 3rd number:
→ Q₁ = 11

#### Find Q₃ (Third Quartile):
Upper half (excluding median):
29, 30, 32, 32, 39 → 5 numbers
Middle is the 3rd number:
→ Q₃ = 32

✔ Answer for Problem 1:
- Minimum: 8
- Maximum: 39
- Q₁: 11
- Q₂: 23
- Q₃: 32

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Problem 2:

Data: 58, 67, 44, 72, 51, 42, 60, 46, 69

#### Step 1: Sort the data
42, 44, 46, 51, 58, 60, 67, 69, 72

There are 9 values (odd)

- Minimum: 42
- Maximum: 72

#### Q₂ (Median):
Middle value is the 5th number:
→ Q₂ = 58

#### Q₁ (First Quartile):
Lower half (first 4 values): 42, 44, 46, 51
Median of these 4: average of 2nd and 3rd
→ (44 + 46)/2 = 45

→ Q₁ = 45

#### Q₃ (Third Quartile):
Upper half (last 4 values): 60, 67, 69, 72
Median: (67 + 69)/2 = 68

→ Q₃ = 68

✔ Answer for Problem 2:
- Minimum: 42
- Maximum: 72
- Q₁: 45
- Q₂: 58
- Q₃: 68

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Problem 3:

Data: 67, 100, 94, 77, 80, 62, 79, 68, 95, 86, 73, 84

#### Step 1: Sort the data
62, 67, 68, 73, 77, 79, 80, 84, 86, 94, 95, 100

There are 12 values (even)

- Minimum: 62
- Maximum: 100

#### Q₂ (Median):
Average of 6th and 7th values:
(79 + 80)/2 = 79.5

→ Q₂ = 79.5

#### Q₁ (First Quartile):
Lower half: 62, 67, 68, 73, 77, 79 → 6 values
Median of this half: average of 3rd and 4th
(68 + 73)/2 = 70.5

→ Q₁ = 70.5

#### Q₃ (Third Quartile):
Upper half: 80, 84, 86, 94, 95, 100 → 6 values
Median: average of 3rd and 4th
(86 + 94)/2 = 90

→ Q₃ = 90

✔ Answer for Problem 3:
- Minimum: 62
- Maximum: 100
- Q₁: 70.5
- Q₂: 79.5
- Q₃: 90

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✔ Final Answers:

#### 1)
- Minimum: 8
- Maximum: 39
- Q₁: 11
- Q₂: 23
- Q₃: 32

#### 2)
- Minimum: 42
- Maximum: 72
- Q₁: 45
- Q₂: 58
- Q₃: 68

#### 3)
- Minimum: 62
- Maximum: 100
- Q₁: 70.5
- Q₂: 79.5
- Q₃: 90

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📊 How to Draw Box-and-Whisker Plot:

For each problem:
1. Draw a number line with appropriate scale.
2. Mark the five values: Min, Q₁, Q₂, Q₃, Max.
3. Draw a box from Q₁ to Q₃.
4. Draw a line inside the box at Q₂.
5. Draw "whiskers" from Q₁ to Min and from Q₃ to Max.

Let me know if you'd like visual sketches or help drawing them!