Worksheet on Range, IQR, and Box and Whisker Plots Practice

Let’s solve each problem step-by-step.

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**1. Would range or IQR be more appropriate in this data set:
32, 35, 76, 29, 30, 32, 31, 39, 28, 34**

✔ Answer: IQR

Explanation:
The data set contains an outlier — 76, which is much larger than the rest of the values (which are mostly in the 28–39 range). The range is sensitive to outliers (Range = Max – Min = 76 – 28 = 48), so it gives a misleading impression of spread. The IQR (Interquartile Range) only looks at the middle 50% of the data (Q3 – Q1), ignoring outliers, making it a more robust and appropriate measure of spread here.

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**2. Find the max, min, Q1, Q2, and Q3 of the data set:
8, 2, 10, 9, 7, 5, 13, 4, 8, 12, 16**

✔ First, sort the data:

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

There are 11 data points.

- Min = smallest value = 2
- Max = largest value = 16
- Q2 (Median) = middle value = 6th value = 8
- Q1 = median of the lower half (first 5 numbers: 2, 4, 5, 7, 8) → median = 5
- Q3 = median of the upper half (last 5 numbers: 9, 10, 12, 13, 16) → median = 12

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

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

The plot shows:
- Left whisker ends at ~3
- Box starts at ~8 → that’s Q1
- Line inside box at ~18 → that’s Q2 (median)
- Box ends at ~30 → that’s Q3
- Right whisker ends at ~45

✔ So label:
- Q1 at 8
- Q2 at 18
- Q3 at 30

Now calculate:

- Range = Max – Min = 45 – 3 = 42
- IQR = Q3 – Q1 = 30 – 8 = 22

✔ Final Answers:
- Q1: 8
- Q2: 18
- Q3: 30
- Range: 42
- IQR: 22

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

- Min = 62
- Max = 109
- Q2 (Median) = 7th value = 85
- Q1 = median of first 6 values: 62, 65, 70, 72, 73, 73 → average of 3rd & 4th = (70 + 72)/2 = 71
- Q3 = median of last 6 values: 89, 91, 95, 99, 106, 109 → average of 3rd & 4th = (95 + 99)/2 = 97

✔ So for the box plot:
- Draw number line from 60 to 110 (as given).
- Mark:
- Left whisker at 62
- Box starts at 71 (Q1)
- Vertical line inside box at 85 (Q2)
- Box ends at 97 (Q3)
- Right whisker at 109

*(You can sketch this on paper or digitally — the key is placing these 5 values correctly.)*

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Box and Whisker Plot for January Temperatures (used for #5–10):

From the plot:
- Left whisker: 33° (lowest temp)
- Q1: 37°
- Q2 (median): 40°
- Q3: 42°
- Right whisker: 43° (highest temp)

*(Note: The dots are at 33 and 43, and the box goes from 37 to 42 with line at 40.)*

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5. What was the lowest temperature recorded?

✔ From the left whisker: 33°F

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

✔ 37° is Q1 → 25% of data is below Q1, so 75% are above Q1.

✔ Answer: 75%

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

✔ 40° is Q2 (median) → 50% of data is above the median.

✔ Answer: 50%

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

✔ From plot:
- Q1 = 37°
- Q3 = 42°

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

✔ 37° is Q1 → 25% of data is below Q1.

✔ Answer: 25%

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10. What was the median temperature in January?

✔ Median = Q2 = 40°F

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## ✔ FINAL ANSWERS SUMMARY:

1. IQR (because of outlier 76)
2. Max: 16, Min: 2, Q1: 5, Q2: 8, Q3: 12
3. Q1=8, Q2=18, Q3=30; Range=42, IQR=22
4. Box plot: Min=62, Q1=71, Q2=85, Q3=97, Max=109
5. 33°F
6. 75%
7. 50%
8. Q1=37°, Q3=42°
9. 25%
10. 40°F

Let me know if you want visuals or further explanation!