AQA GCSE · Question 09.3 · Data Visualization and Representation
The box plots for the two samples are shown on the same grid. Use the box plots to compare the two samples. Make two comparisons.
How to approach this question
1. **Identify key values from the box plots**:
* **Old Sample**: Median (red line) = 1. Q1 (left edge of box) = 1. Q3 (right edge of box) = 2. IQR = 2 - 1 = 1.
* **New Sample**: Median = 2. Q1 = 1. Q3 = 3. IQR = 3 - 1 = 2.
2. **Compare the Medians**: Look at the red lines. The median for the new sample (2) is higher than for the old sample (1). Write a sentence explaining what this means in context (e.g., "on average, customers in the new sample got more rewards").
3. **Compare a measure of spread (IQR or Range)**:
* **IQR**: The box for the new sample (width from 1 to 3, so IQR=2) is wider than the box for the old sample (width from 1 to 2, so IQR=1). Write a sentence explaining what this means (e.g., "the number of rewards was more spread out/varied for the new sample").
* **Range**: The range is Max - Min. For both samples, Min=1 and Max=5, so the range is 4. The ranges are the same, so this is a less useful comparison.
4. Formulate two distinct comparison statements, one about the average (median) and one about the spread (IQR).
Full Answer
**Comparison 1 (Median):**
The median number of rewards for the new sample (Median = 2) is higher than the median for the old sample (Median = 1). This indicates that, on average, customers achieved more rewards under the new system.
**Comparison 2 (Interquartile Range):**
The interquartile range for the new sample (IQR = 3 - 1 = 2) is larger than the IQR for the old sample (IQR = 2 - 1 = 1). This shows that the number of rewards was more spread out or less consistent for the middle 50% of customers in the new sample.
When comparing box plots, you should comment on a measure of central tendency (the median) and a measure of spread (the interquartile range or range).
**Comparison 1: Median (A measure of average)**
- From the box plots, the median for the **Old Sample** is 1 reward.
- The median for the **New Sample** is 2 rewards.
- **Conclusion**: The median number of rewards is higher for the new sample. This suggests that the new reward system was successful in increasing the average number of rewards customers achieved.
**Comparison 2: Interquartile Range (A measure of spread)**
- For the **Old Sample**, the IQR = Q3 - Q1 = 2 - 1 = 1.
- For the **New Sample**, the IQR = Q3 - Q1 = 3 - 1 = 2.
- **Conclusion**: The interquartile range is larger for the new sample. This indicates that there is more variation or a wider spread in the number of rewards achieved by the middle 50% of customers under the new system.
Common mistakes
✗ Only stating the values (e.g., "The median is 1 and 2") without making a comparison (e.g., "...so the median is higher for the new sample").
✗ Only making one comparison when two are asked for.
✗ Confusing the median with the mean, or the IQR with the range.
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