Box Plot Worksheets | Free - CommonCoreSheets - Free Printable

Let's solve each problem step by step to create a box plot (also known as a box-and-whisker plot) for each set of numbers. A box plot requires the following five-number summary:

1. Minimum – smallest value
2. First Quartile (Q1) – median of the lower half
3. Median (Q2) – middle value of the data set
4. Third Quartile (Q3) – median of the upper half
5. Maximum – largest value

We will go through each set, sort the numbers, find these five values, and then sketch the box plot on the given number line.

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Problem 1:

Data: 57, 81, 33, 30, 38, 40, 51, 91

#### Step 1: Sort the data
30, 33, 38, 40, 51, 57, 81, 91

#### Step 2: Find the five-number summary
- Min = 30
- Max = 91
- Median (Q2): Since there are 8 values (even), median is average of 4th and 5th:
- (40 + 51)/2 = 45.5
- Q1 (lower half): First 4 numbers: 30, 33, 38, 40 → median = (33 + 38)/2 = 35.5
- Q3 (upper half): Last 4 numbers: 51, 57, 81, 91 → median = (57 + 81)/2 = 69

✔ Five-number summary:
Min = 30, Q1 = 35.5, Median = 45.5, Q3 = 69, Max = 91

#### Box Plot on Number Line (25–100):
- Draw a box from 35.5 to 69
- Draw a line at 45.5 inside the box
- Whiskers extend from 30 to 91

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Problem 2:

Data: 74, 65, 93, 71, 58, 82, 63, 89

#### Step 1: Sort
58, 63, 65, 71, 74, 82, 89, 93

#### Step 2: Five-number summary
- Min = 58
- Max = 93
- Median = (71 + 74)/2 = 72.5
- Q1: Lower half: 58, 63, 65, 71 → median = (63 + 65)/2 = 64
- Q3: Upper half: 74, 82, 89, 93 → median = (82 + 89)/2 = 85.5

✔ Summary:
Min = 58, Q1 = 64, Median = 72.5, Q3 = 85.5, Max = 93

#### Box Plot (55–100)
- Box from 64 to 85.5
- Median line at 72.5
- Whiskers from 58 to 93

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Problem 3:

Data: 54, 20, 79, 53, 55, 42, 45, 39, 53, 82, 50

#### Step 1: Sort
20, 39, 42, 45, 50, 53, 53, 54, 55, 79, 82

(11 values)

#### Step 2: Five-number summary
- Min = 20
- Max = 82
- Median = 6th value = 53
- Q1: Lower half (first 5): 20, 39, 42, 45, 50 → median = 42
- Q3: Upper half (last 5): 54, 55, 79, 82 → wait, 5 values: 53, 54, 55, 79, 82 → median = 55

✔ Summary:
Min = 20, Q1 = 42, Median = 53, Q3 = 55, Max = 82

#### Box Plot (15–85)
- Box from 42 to 55
- Median line at 53
- Whiskers from 20 to 82

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Problem 4:

Data: 14, 12, 15, 7, 5, 8, 19

#### Step 1: Sort
5, 7, 8, 12, 14, 15, 19

(7 values)

#### Step 2: Five-number summary
- Min = 5
- Max = 19
- Median = 4th value = 12
- Q1: Lower half: 5, 7, 8 → median = 7
- Q3: Upper half: 14, 15, 19 → median = 15

✔ Summary:
Min = 5, Q1 = 7, Median = 12, Q3 = 15, Max = 19

#### Box Plot (0–25)
- Box from 7 to 15
- Median line at 12
- Whiskers from 5 to 19

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Problem 5:

Data: 10, 19, 10, 6, 14, 13, 19

#### Step 1: Sort
6, 10, 10, 13, 14, 19, 19

(7 values)

#### Step 2: Five-number summary
- Min = 6
- Max = 19
- Median = 4th value = 13
- Q1: Lower half: 6, 10, 10 → median = 10
- Q3: Upper half: 14, 19, 19 → median = 19

✔ Summary:
Min = 6, Q1 = 10, Median = 13, Q3 = 19, Max = 19

#### Box Plot (-5 to 25)
- Box from 10 to 19
- Median line at 13
- Whiskers from 6 to 19

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Problem 6:

Data: 7, 6, 5, 14, 18, 14, 20

#### Step 1: Sort
5, 6, 7, 14, 14, 18, 20

(7 values)

#### Step 2: Five-number summary
- Min = 5
- Max = 20
- Median = 4th value = 14
- Q1: Lower half: 5, 6, 7 → median = 6
- Q3: Upper half: 14, 18, 20 → median = 18

✔ Summary:
Min = 5, Q1 = 6, Median = 14, Q3 = 18, Max = 20

#### Box Plot (0–35)
- Box from 6 to 18
- Median line at 14
- Whiskers from 5 to 20

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Problem 7:

Data: 89, 59, 94, 64, 92, 72, 85, 59, 99, 52

#### Step 1: Sort
52, 59, 59, 64, 72, 85, 89, 92, 94, 99

(10 values)

#### Step 2: Five-number summary
- Min = 52
- Max = 99
- Median = (5th + 6th)/2 = (72 + 85)/2 = 78.5
- Q1: Lower half: 52, 59, 59, 64, 72 → median = 59
- Q3: Upper half: 85, 89, 92, 94, 99 → median = 92

✔ Summary:
Min = 52, Q1 = 59, Median = 78.5, Q3 = 92, Max = 99

#### Box Plot (40–105)
- Box from 59 to 92
- Median line at 78.5
- Whiskers from 52 to 99

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✔ Final Answer Summary:

| Problem | Min | Q1 | Median | Q3 | Max |
|--------|-----|----|--------|----|-----|
| 1 | 30 | 35.5 | 45.5 | 69 | 91 |
| 2 | 58 | 64 | 72.5 | 85.5 | 93 |
| 3 | 20 | 42 | 53 | 55 | 82 |
| 4 | 5 | 7 | 12 | 15 | 19 |
| 5 | 6 | 10 | 13 | 19 | 19 |
| 6 | 5 | 6 | 14 | 18 | 20 |
| 7 | 52 | 59 | 78.5 | 92 | 99 |

To complete the worksheet, you would now draw each box plot on the provided number lines using these values. Each box plot should have:
- A box from Q1 to Q3
- A line inside the box at the median
- Whiskers extending from min to max

Let me know if you'd like a visual sketch or explanation of how to draw one!