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AQA GCSE · Question 16 · Statistics
The table shows information about the ages of members of two clubs.
Compare the average age and consistency of ages for the members of the two clubs.
Average:
Consistency:
<br/><br/>
<table border="1" cellpadding="15" cellspacing="0" style="border-collapse: collapse; font-family: Arial, sans-serif; font-size: 18px;">
<tr>
<th></th>
<th>Median age (years)</th>
<th>Interquartile range<br>of ages (years)</th>
</tr>
<tr>
<td>Swimming club</td>
<td style="text-align: center;">21.2</td>
<td style="text-align: center;">7.3</td>
</tr>
<tr>
<td>Cycling club</td>
<td style="text-align: center;">29.7</td>
<td style="text-align: center;">4.6</td>
</tr>
</table>
The table shows information about the ages of members of two clubs.
Compare the average age and consistency of ages for the members of the two clubs.
Average:
Consistency:
<br/><br/>
<table border="1" cellpadding="15" cellspacing="0" style="border-collapse: collapse; font-family: Arial, sans-serif; font-size: 18px;"> <tr> <th></th> <th>Median age (years)</th> <th>Interquartile range<br>of ages (years)</th> </tr> <tr> <td>Swimming club</td> <td style="text-align: center;">21.2</td> <td style="text-align: center;">7.3</td> </tr> <tr> <td>Cycling club</td> <td style="text-align: center;">29.7</td> <td style="text-align: center;">4.6</td> </tr> </table>How to approach this question
1. **Compare the Averages:** The median is a type of average. Compare the median age for the swimming club and the cycling club. State which is higher and what this means in the context of the question (i.e., which club has older members on average).
2. **Compare the Consistency:** The interquartile range (IQR) is a measure of spread or consistency. A smaller IQR means the data is more consistent (less spread out). Compare the IQRs for the two clubs. State which is smaller and what this means in context (i.e., which club has more consistent ages).
Full Answer
**Average:**
The median age of the cycling club (29.7) is higher than the median age of the swimming club (21.2). This suggests that, on average, the members of the cycling club are older.
**Consistency:**
The interquartile range (IQR) of the cycling club (4.6) is smaller than the IQR of the swimming club (7.3). A smaller IQR means the data is less spread out, so the ages of the members of the cycling club are more consistent.
This question asks for a comparison of two data sets using the median and interquartile range (IQR).
**Average:**
The median is used to compare the average age.
- Swimming club median = 21.2 years.
- Cycling club median = 29.7 years.
Since 29.7 > 21.2, the members of the cycling club are, on average, older than the members of the swimming club.
**Consistency:**
The interquartile range (IQR) is used to compare the consistency or spread of ages. A smaller IQR indicates that the ages are more closely clustered together, meaning they are more consistent.
- Swimming club IQR = 7.3 years.
- Cycling club IQR = 4.6 years.
Since 4.6 < 7.3, the cycling club has a smaller IQR. This means the ages of the members in the cycling club are more consistent (less spread out) than the ages in the swimming club.
Common mistakes
✗ Just stating the numbers without interpreting them (e.g., "29.7 is bigger than 21.2"). You must relate it to the context of age.
✗ Confusing the measures, e.g., saying the median shows consistency.
✗ Misinterpreting the IQR, e.g., saying a larger IQR means more consistent.
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