Let’s go step by step through each problem.
---
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. The number
76 is much bigger than the rest (which are mostly between 28 and 39). That means it’s an outlier.
- Range = max - min → affected by outliers.
- IQR = Q3 - Q1 → not affected by outliers.
Since there’s an outlier (76),
IQR is more appropriate because it gives a better idea of the spread of the middle part of the data.
✔ Final Answer for #1:
IQR
---
Problem 2: Find max, min, Q1, Q2, Q3 for this data set.
Data:
8, 2, 10, 9, 7, 5, 13, 4, 8, 12, 16
Step 1: Sort the data from smallest to largest:
→ 2, 4, 5, 7, 8, 8, 9, 10, 12, 13, 16
There are 11 numbers.
- Min = first number =
2
- Max = last number =
16
- Q2 (median) = middle number → since 11 numbers, the 6th one →
8
Now split into two halves (excluding the median):
Lower half: 2, 4, 5, 7, 8 → median of this is
5 → Q1 =
5
Upper half: 9, 10, 12, 13, 16 → median of this is
12 → Q3 =
12
✔ Final Answers for #2:
Max:
16
Min:
2
Q1:
5
Q2:
8
Q3:
12
---
Problem 3: Label Q1, Q2, Q3 on the box plot. Then find range and IQR.
Looking at the box plot:
The number line goes from 0 to 50.
From the plot:
- Left whisker end (min) =
5
- Right whisker end (max) =
45
- Left edge of box (Q1) =
10
- Line inside box (Q2/median) =
15
- Right edge of box (Q3) =
30
So label them as:
- 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
---
Problem 4: Draw a box and whisker plot using this 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
Total = 13 numbers.
Find:
- Min =
62
- Max =
109
- Q2 (median) = 7th number →
85
Split into lower and upper halves (exclude median):
Lower half: 62, 65, 70, 72, 73, 73 → 6 numbers → median is average of 3rd and 4th → (70 + 72)/2 =
71 → Q1 =
71
Upper half: 89, 91, 95, 99, 106, 109 → median = average of 3rd and 4th → (95 + 99)/2 =
97 → Q3 =
97
So five-number summary:
Min = 62, Q1 = 71, Q2 = 85, Q3 = 97, Max = 109
To draw the plot on the given number line (60 to 110):
- Put a dot at 62 (min)
- Put a dot at 109 (max)
- Draw a box from 71 to 97
- Draw a line inside the box at 85
- Connect dots to box with lines (whiskers)
You can sketch it like that — but since we’re writing answers, just know these values are correct.
✔ Final Answers for #4 (values needed to draw):
Min =
62, Q1 =
71, Q2 =
85, Q3 =
97, Max =
109
---
Problems 5–10: Use the box plot showing daily temperatures in January.
Box plot shown has:
Number line: 32 to 44
From the plot:
- Min (left whisker) =
35
- Q1 (left edge of box) =
37
- Q2 (line in box) =
40
- Q3 (right edge of box) =
42
- Max (right whisker) =
43
(We can read these directly off the plot.)
---
#5: What was the lowest temperature recorded?
That’s the minimum →
35°
✔ Answer:
35
---
#6: What percentage of temperatures were above 37°?
37° is Q1 → which means 25% of data is below it, so
75% is above it.
✔ Answer:
75%
---
#7: What percentage of temperatures were above 40°?
40° is the median (Q2) → 50% of data is above it.
✔ Answer:
50%
---
#8: What is Q1 and Q3 for this data set?
From the plot:
- Q1 =
37
- Q3 =
42
✔ Answer: Q1 =
37, Q3 =
42
---
#9: What percentage of temperatures were below 37°?
37° is Q1 → 25% of data is below it.
✔ Answer:
25%
---
#10: What was the median temperature in January?
Median is Q2 →
40°
✔ Answer:
40
---
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. Min: 62, Q1: 71, Q2: 85, Q3: 97, Max: 109
5. 35
6. 75%
7. 50%
8. Q1: 37, Q3: 42
9. 25%
10. 40
Parent Tip: Review the logic above to help your child master the concept of worksheet on box and whisker plots.
