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

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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.

- The range = max - min = 76 - 28 = 48
- The IQR (Interquartile Range) is resistant to outliers and measures the spread of the middle 50% of the data.

Because there's an outlier, the IQR is more appropriate than the range.

✔ Answer: IQR is more appropriate because the data has an outlier (76).

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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

#### Step 2: Find Q2 (Median)
The median is the 6th value:
→ Q2 = 8

#### Step 3: Find Q1 (First Quartile)
Lower half (excluding median):
2, 4, 5, 7, 8
Median of lower half = 5 → Q1 = 5

#### Step 4: Find Q3 (Third Quartile)
Upper half (excluding median):
9, 10, 12, 13, 16
Median of upper half = 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 the range and IQR.

Given box plot:

```
●─────────┬─────────┬─────────●
0 10 20 30 40 50
```

From the plot:
- Left whisker starts at 0 → Min = 0
- Box starts at 5 → Q1 = 5
- Middle line at 15 → Q2 = 15
- Box ends at 30 → Q3 = 30
- Right whisker ends at 45 → Max = 45

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

✔ Labeling:
- 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

→ 13 values (odd)

- Min = 62
- Max = 109

#### Step 2: Find Q2 (Median)
Middle value (7th): 85 → Q2 = 85

#### Step 3: Find Q1 (Lower quartile)
Lower half (first 6 values):
62, 65, 70, 72, 73, 73
Median of these: average of 3rd and 4th → (70 + 72)/2 = 71 → Q1 = 71

#### Step 4: Find Q3 (Upper quartile)
Upper half (last 6 values):
89, 91, 95, 99, 106, 109
Median: (95 + 99)/2 = 97 → Q3 = 97

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 and Whisker Plot:
```
┌───────────────┐
│ │
●─────┤ ├────●
│ │
└───────────────┘
60 70 80 90 100 110
↑ ↑ ↑ ↑ ↑ ↑
62 71 85 97 109
```

(Plot should have:
- Left whisker to 62
- Box from 71 to 97
- Median line at 85
- Right whisker to 109)

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5–10. Use the given box and whisker plot for January temperatures

Given plot:
```
●─────────┬─────────┬─────────●
32 36 38 40 42 44
```

From the plot:
- Left whisker: 35 → Min = 35
- Box starts at 37 → Q1 = 37
- Median line at 40 → Q2 = 40
- Box ends at 42 → Q3 = 42
- Right whisker: 43 → Max = 43

Wait! Let's double-check based on tick marks:

The axis goes: 32, 36, 38, 40, 42, 44

But the left dot is just after 32 → looks like 35
The right dot is just before 44 → likely 43

And:
- Left end of box: between 36 and 38 → 37
- Median: at 40
- Right end of box: at 42

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

Now answer questions:

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