To compare the two distributions (Maths Exam and Science Exam) using the box and whisker diagrams, we need to look at three key things for each:
1.
Median – the middle value (shown by the line inside the box)
2.
Interquartile Range (IQR) – the width of the box (Q3 - Q1), which shows how spread out the middle 50% of scores are
3.
Overall Spread / Range – from the leftmost whisker (minimum) to the rightmost whisker (maximum)
Let’s read the values from the diagram carefully.
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Maths Exam (blue box):
- Minimum (left end of whisker): ~45
- Q1 (left edge of box): ~55
- Median (line in box): ~65
- Q3 (right edge of box): ~75
- Maximum (right end of whisker): ~95
→ IQR = Q3 - Q1 = 75 - 55 =
20
→ Range = Max - Min = 95 - 45 =
50
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Science Exam (yellow box):
- Minimum: ~30
- Q1: ~45
- Median: ~55
- Q3: ~70
- Maximum: ~85
→ IQR = 70 - 45 =
25
→ Range = 85 - 30 =
55
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Comparison:
✔ Median:
Maths median is 65, Science median is 55 → Students scored higher on average in Maths.
✔ IQR (spread of middle 50%):
Maths IQR = 20, Science IQR = 25 → The middle half of Maths scores are more tightly grouped; Science scores are more spread out in the middle.
✔ Range (total spread):
Maths range = 50, Science range = 55 → Science has a wider overall spread — some students did much worse or better than others compared to Maths.
✔ Shape/Skew?
Both boxes look fairly symmetric, but Science’s lower whisker goes down to 30 while Maths starts at 45 — so Science has more low outliers or extreme low scores.
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Final Summary:
Students generally performed better in the Maths exam (higher median). Their scores were also more consistent in the middle 50% (smaller IQR). However, the Science exam had a wider total range, meaning there was more variation — including some very low scores not seen in Maths.
Final Answer:
The Maths exam has a higher median (65 vs 55), smaller interquartile range (20 vs 25), and smaller overall range (50 vs 55) than the Science exam. This means students scored better and more consistently in Maths, while Science scores were more spread out with some very low results.
Parent Tip: Review the logic above to help your child master the concept of box and whiskers math.
