Let’s solve each problem step by step, using the box plots provided.
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Problem 1: Compare IQR values for Section A and Section B
What is IQR?
IQR stands for
Interquartile Range. It is the difference between the
third quartile (Q3) and the
first quartile (Q1):
>
IQR = Q3 – Q1
The IQR represents the middle 50% of the data — it tells us how spread out the central portion of the data is.
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Step 1: Read Q1 and Q3 from the box plots
Looking at the box plot for
Section A:
- The left edge of the box (Q1) is at
12.
- The right edge of the box (Q3) is at
22.
→ So, IQR for Section A = 22 – 12 =
10
Looking at the box plot for
Section B:
- The left edge of the box (Q1) is at
14.
- The right edge of the box (Q3) is at
24.
→ So, IQR for Section B = 24 – 14 =
10
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Conclusion for Problem 1:
✔ The IQR values for both Section A and Section B are equal (both are 10).
This means that the middle 50% of students in both sections spent a similar amount of time reading — the spread of the central half of the data is identical.
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Problem 2: Compare range values for Morning and Evening park visitors
What is Range?
Range =
Maximum value – Minimum value
It shows the total spread of the data from the lowest to the highest value.
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Step 1: Read min and max from the box plots
Looking at the box plot for
Morning:
- Minimum (left whisker):
22
- Maximum (right whisker):
70
→ Range = 70 – 22 =
48
Looking at the box plot for
Evening:
- Minimum (left whisker):
26
- Maximum (right whisker):
74
→ Range = 74 – 26 =
48
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Conclusion for Problem 2:
✔ The range values for both Morning and Evening are equal (both are 48).
This means that the overall spread of visitor numbers — from the fewest to the most visitors — is the same for both time periods.
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✔ Final Answers:
1. Answer:
*The IQR values for Section A and Section B are the same. Both have an IQR of 10, meaning the middle 50% of students in each section spent a similar amount of time reading during the holidays.*
2. Answer:
*The range values for Morning and Evening park visitors are the same. Both have a range of 48, meaning the total spread of visitor numbers (from minimum to maximum) is identical for both time periods.*
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Let me know if you’d like to compare medians or other features too!
Parent Tip: Review the logic above to help your child master the concept of box plots worksheet.
