Box Plot Analysis

Name:

Date:

📊 Part 1: Understanding Box Plots

Rugby Scores Data: The Auckland Blues scored these points in their last 12 matches: 15, 23, 31, 18, 27, 45, 22, 19, 28, 33, 21, 26

1. What type of data is represented by rugby scores?

Categorical data

Discrete numerical data

Continuous numerical data

2. From the rugby scores above, identify the following values:

Minimum: _______ Maximum: _______ Range: _______

Median (Q2): _______ Lower Quartile (Q1): _______ Upper Quartile (Q3): _______

3. The temperature data below shows daily highs in Auckland over 15 days (°C):
18, 22, 19, 25, 28, 17, 21, 24, 26, 20, 23, 29, 19, 22, 31

What type of data is temperature?

Categorical data

Discrete numerical data

Continuous numerical data

4. Which of these would be considered outliers in a box plot? (Check all that apply)

Values beyond 1.5 × IQR from the quartiles

The median value

Unusually high or low values

Values exactly at the quartiles

🔍 Part 2: Comparing Box Plots

Scenario: Two cricket teams' bowling speeds (km/h) are shown in box plots:

Team A: Min=110, Q1=125, Median=135, Q3=145, Max=160

Team B: Min=120, Q1=130, Median=140, Q3=150, Max=170

5. Calculate the Interquartile Range (IQR) for both teams:

Team A IQR: _______ km/h

Team B IQR: _______ km/h

6. Which team has greater variability in bowling speeds? Explain your reasoning:

7. Compare the median bowling speeds. What can you conclude about the typical performance of each team?

🎯 Part 3: Extension & Analysis

8. Advanced Challenge: A netball team's goal percentages over 20 games show: Q1=65%, Median=72%, Q3=80%. If any value below 41.5% or above 103.5% is an outlier, what is the team's IQR and outlier boundaries?

9. Real-world Application: You're analysing rainfall data (mm) for two New Zealand cities. City X has a larger IQR than City Y, but the same median. What does this tell you about rainfall patterns in each city?

10. Design Challenge: Create your own data set of 10 values representing something you're interested in (gaming scores, workout times, etc.). Calculate the five-number summary:

Data type: _________________ (categorical/discrete/continuous)

Your data: ________________________________________________

Min: _____ Q1: _____ Median: _____ Q3: _____ Max: _____