Practice worksheet for understanding range, IQR, and box and whisker plots with exercises and a sample plot.

Let’s solve each problem step by step.

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

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

First, let’s look for outliers. Sort the data:

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

See that 76? It’s way bigger than the rest — it’s an outlier.

- Range = max - min → affected by outliers.
- IQR (Interquartile Range) = Q3 - Q1 → ignores outliers, focuses on middle 50%.

Since there’s an outlier (76), IQR is more appropriate.

✔ Final Answer for #1: IQR

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Problem 2: Find max, min, Q1, Q2, 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 numbers.

- Min = smallest = 2
- Max = largest = 16
- Q2 (median) = middle number → 6th number = 8

Now split into lower and upper halves (exclude median since odd count):

Lower half: 2, 4, 5, 7, 8 → median of this = 5 → Q1
Upper half: 9, 10, 12, 13, 16 → median of this = 12 → Q3

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

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Problem 3: Label Q1, Q2, Q3 on box plot. Then find range and IQR.

Box plot shown with number line from 0 to 50.

From the plot:

- Left whisker end (min) = 5
- Left edge of box (Q1) = 10
- Line inside box (Q2/median) = 15
- Right edge of box (Q3) = 30
- Right whisker end (max) = 45

So label:
- Q1 = 10
- Q2 = 15
- Q3 = 30

Range = max - min = 45 - 5 = 40

IQR = Q3 - Q1 = 30 - 10 = 20

✔ Final Answers for #3:
Q1: 10, Q2: 15, Q3: 30
Range: 40, IQR: 20

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Problem 4: Draw a box and whisker plot using the 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

Count = 13 numbers → odd

- Min = 62
- Max = 109
- Median (Q2) = 7th number = 85

Split into lower and upper halves (exclude median):

Lower: 62, 65, 70, 72, 73, 73 → 6 numbers → median between 3rd and 4th: (70 + 72)/2 = 71 → Q1
Upper: 89, 91, 95, 99, 106, 109 → median between 3rd and 4th: (95 + 99)/2 = 97 → Q3

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

To draw the plot on the given number line (60 to 110):

- Put dot at 62 (min)
- Box starts at 71 (Q1)
- Line inside box at 85 (Q2)
- Box ends at 97 (Q3)
- Dot at 109 (max)
- Connect dots to box with lines (whiskers)

✔ Final Answer for #4:
Draw box plot with:
Min=62, Q1=71, Median=85, Q3=97, Max=109

*(Since you can’t draw here, just know these values go on the number line as described.)*

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Problems 5–10: Use the box plot showing daily temperatures in January.

Box plot number line: 32 to 44

From the plot:

- Min (left whisker) = 34
- Q1 (left edge of box) = 37
- Median (line in box) = 40
- Q3 (right edge of box) = 42
- Max (right whisker) = 43

Wait — let me double-check based on tick marks.

Number line has ticks at: 32, 36, 38, 40, 42, 44 → so each big tick is 2 units? But there are small ticks too.

Looking again: between 32 and 36, there are two small ticks → so each small tick = 1 unit.

So:

- Left whisker ends at first small tick after 32 → that’s 33? Wait no — let's count carefully.

Actually, looking at the plot description:

The left whisker goes to a point aligned with the first mark after 32 — which should be 33? But wait — maybe it’s 34?

Hold on — standard interpretation: if the number line shows 32, then next mark is 33, then 34, etc., up to 44.

But in the image, the left whisker ends at the second mark after 32 → that would be 34.

Similarly:

- Q1 (left side of box) aligns with 37? Let’s see: from 36 to 38, middle is 37 → yes, box starts at 37.
- Median line is at 40 → clear.
- Q3 (right side of box) is at 42 → clear.
- Right whisker ends at 43 (one before 44).

So confirmed:

- Min = 34
- Q1 = 37
- Median = 40
- Q3 = 42
- Max = 43

Now answer questions:

#5: What was the lowest temperature recorded?
→ Min = 34°

#6: What percentage of temperatures were above 37°?
37° is Q1 → means 25% of data is below Q1, so 75% is above Q1.
→ 75%

#7: What percentage of temperatures were above 40°?
40° is median → 50% above, 50% below.
→ 50%

#8: What is Q1 and Q3?
Q1 = 37, Q3 = 42

#9: What percentage were below 37°?
Below Q1 → 25%

#10: What was the median temperature?
Median = 40°

✔ Final Answers for #5–10:
5. 34°
6. 75%
7. 50%
8. Q1: 37, Q3: 42
9. 25%
10. 40°

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Final Answer:
1. IQR
2. Max: 16, Min: 2, Q1: 5, Q2: 8, Q3: 12
3. Q1: 10, Q2: 15, Q3: 30; Range: 40, IQR: 20
4. Box plot with Min=62, Q1=71, Median=85, Q3=97, Max=109
5. 34°
6. 75%
7. 50%
8. Q1: 37, Q3: 42
9. 25%
10. 40°