The image shows
two box plots comparing the
final grades in AP Calculus from 2011 to 2021 for two cities:
Edmonton and
Calgary. We will analyze and interpret the data shown in these box plots.
---
🔍 Understanding Box Plots
A box plot displays five key statistics:
-
Minimum (left whisker)
-
First Quartile (Q1) (bottom of the box)
-
Median (Q2) (line inside the box)
-
Third Quartile (Q3) (top of the box)
-
Maximum (right whisker)
The
interquartile range (IQR) is Q3 – Q1, representing the middle 50% of the data.
---
📊 Analysis of the Box Plots
####
1. Edmonton
-
Min: ~45
-
Q1: ~60
-
Median: ~75
-
Q3: ~80
-
Max: ~90
####
2. Calgary
-
Min: ~40
-
Q1: ~60
-
Median: ~75
-
Q3: ~85
-
Max: ~100
---
✔ Key Observations & Comparisons
| Feature | Edmonton | Calgary |
|--------|---------|--------|
|
Median | 75 | 75 |
|
Range | 45–90 = 45 | 40–100 = 60 |
|
IQR | 80 – 60 = 20 | 85 – 60 = 25 |
|
Spread | Narrower | Wider |
|
Outliers | None visible | None visible |
---
🔎 Interpretation
1.
Same Median (75):
- The central tendency of final grades is
identical in both cities.
- Half of students in each city scored
above 75, half below.
2.
Different Spreads:
-
Calgary has a
wider spread (range = 60) than Edmonton (range = 45), indicating greater variability in student performance.
- Calgary also has a
larger IQR (25 vs. 20), meaning the middle 50% of students in Calgary had more variation in scores.
3.
Higher Maximum in Calgary:
- Calgary has a few students scoring up to
100, while Edmonton's highest is around
90.
- This suggests Calgary may have more high-achieving students.
4.
Lower Minimum in Calgary:
- Calgary has a slightly lower minimum (~40 vs. ~45), indicating some students performed worse.
5.
Similar Lower Quartile (Q1):
- Both cities have Q1 at ~60, so the bottom 25% of students scored similarly.
---
🧠 Conclusion
-
Overall performance is similar in both cities (same median).
-
Calgary shows
greater variability in student performance — more top scorers and more low scorers.
-
Edmonton has a
tighter distribution, with fewer extreme scores.
- Both cities have comparable
lower performance levels, but Calgary has
higher potential for top achievement.
---
💡 Final Answer:
>
The final AP Calculus grades for Edmonton and Calgary (2011–2021) show identical medians (75), indicating similar average performance. However, Calgary exhibits greater variability in scores, with a wider range and higher maximum grade (up to 100), suggesting a broader spectrum of student outcomes. Edmonton’s scores are more tightly clustered, reflecting less variation.
Let me know if you'd like this summarized into a chart or visual explanation!
Parent Tip: Review the logic above to help your child master the concept of box and whisker diagram.
