Box and Whisker Plots Notes and Worksheets - Lindsay Bowden - Free Printable

Let's solve each problem step by step with clear explanations.

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1. Would range or IQR be more appropriate in this data set?

Data:
32, 35, 76, 29, 30, 32, 31, 39, 28, 34

#### Step 1: Look for outliers
Sort the data:
28, 29, 30, 31, 32, 32, 34, 35, 39, 76

Notice that 76 is much higher than the rest — it’s an outlier.

- Range = Max - Min = 76 - 28 = 48 → highly affected by the outlier.
- IQR (Interquartile Range) = Q3 - Q1 → only considers middle 50% of data, so less affected by outliers.

✔ Answer: IQR is more appropriate because the data has an outlier (76), and IQR is resistant to outliers.

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2. Find the max, min, Q1, Q2, and Q3 of the data set

Data:
8, 2, 10, 9, 7, 5, 13, 4, 8, 12, 16

#### Step 1: Sort the data
2, 4, 5, 7, 8, 8, 9, 10, 12, 13, 16

There are 11 values (odd number).

- Min: 2
- Max: 16
- Q2 (Median): The 6th value → 8

Now find Q1 and Q3:

- Lower half (below median): 2, 4, 5, 7, 8 → 5 numbers → Median is 5 → Q1 = 5
- Upper half (above median): 9, 10, 12, 13, 16 → 5 numbers → Median is 12 → Q3 = 12

✔ Answers:
- Max: 16
- Min: 2
- Q1: 5
- Q2: 8
- Q3: 12

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3. Label Q1, Q2, Q3 on the box and whisker plot. Then find range and IQR.

The plot shows:
- Left whisker starts at 0
- Box from ~5 to 30
- Line inside box at 15
- Right whisker ends at 45

From visual:
- Min = 0
- Q1 ≈ 5
- Q2 (median) ≈ 15
- Q3 ≈ 30
- Max = 45

#### Now calculate:
- Range = Max - Min = 45 - 0 = 45
- IQR = Q3 - Q1 = 30 - 5 = 25

✔ Labels:
- Q1: 5
- Q2: 15
- Q3: 30

✔ Range: 45, IQR: 25

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4. Draw a box and whisker plot using the following data:

Data:
62, 73, 65, 70, 72, 95, 109, 106, 99, 73, 85, 89, 91

#### Step 1: Sort the data
62, 65, 70, 72, 73, 73, 85, 89, 91, 95, 99, 106, 109

There are 13 values (odd)

- Min: 62
- Max: 109
- Q2 (Median): 7th value → 85

Now split:
- Lower half: 62, 65, 70, 72, 73, 73 → 6 values → Q1 = average of 3rd and 4th: (70 + 72)/2 = 71
- Upper half: 89, 91, 95, 99, 106, 109 → 6 values → Q3 = average of 3rd and 4th: (95 + 99)/2 = 97

So:
- Min: 62
- Q1: 71
- Q2: 85
- Q3: 97
- Max: 109

Now draw the box plot on the number line from 60 to 110:
- Whiskers: from 62 to 109
- Box from 71 to 97
- Line at 85

✔ Box Plot Summary:
- Left whisker: 62
- Box starts at 71
- Median line at 85
- Box ends at 97
- Right whisker: 109

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5–10: Use the given box and whisker plot (January temperatures)

Plot shows:
- Min: 35 (left end of whisker)
- Q1: 37 (left side of box)
- Median (Q2): 40 (line in box)
- Q3: 42 (right side of box)
- Max: 43 (right end of whisker)

Wait! Looking closely:
- The left whisker starts at 35? But the tick marks start at 32.
- The dot is at 35, then box starts at 37, ends at 42, median at 40, right whisker to 43

But the first dot is at 35, not 32. So:
- Min = 35
- Q1 = 37
- Q2 = 40
- Q3 = 42
- Max = 43

Wait — the whisker goes from 35 to 43, but the box is from 37 to 42, with median at 40.

So:
- Min: 35
- Q1: 37
- Q2: 40
- Q3: 42
- Max: 43

Now answer the questions:

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5. What was the lowest temperature recorded?

→ Min = 35°F

✔ Answer: 35°F

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6. What percentage of the temperatures were above 37°?

Q1 = 37 → 25% of data is below Q1 → so 75% is above Q1.

So, 75% of temperatures were above 37°F.

✔ Answer: 75%

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7. What percentage of the temperatures were above 40°?

Median = 40 → 50% of data is above median.

✔ Answer: 50%

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8. What is the Q1 and Q3 for this data set?

From plot:
- Q1 = 37
- Q3 = 42

✔ Answer: Q1 = 37, Q3 = 42

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9. What percentage of the temperatures were below 37°?

Q1 = 37 → 25% of data is below Q1.

✔ Answer: 25%

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10. What was the median temperature in January?

Median = Q2 = 40°F

✔ Answer: 40°F

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✔ Final Answers:

| Question | Answer |
|--------|--------|
| 1 | IQR (because of outlier) |
| 2 | Max: 16, Min: 2, Q1: 5, Q2: 8, Q3: 12 |
| 3 | Q1=5, Q2=15, Q3=30; Range=45, IQR=25 |
| 4 | Box plot with Min=62, Q1=71, Q2=85, Q3=97, Max=109 |
| 5 | 35°F |
| 6 | 75% |
| 7 | 50% |
| 8 | Q1=37, Q3=42 |
| 9 | 25% |
| 10 | 40°F |

Let me know if you'd like a visual sketch of the box plots!