https://file.aiquickdraw.com/mathbot/file/1728929034279lim0dipp.jpg

Let's break down the information from the image you uploaded.

1. **Cumulative Frequency Graph**: The graph represents the cumulative number of students on the y-axis and the marks on the x-axis. The total number of candidates is 8400.

2. **Finding the Median**:
   - The median corresponds to the 50th percentile, or the value at the 4200th candidate (since 50% of 8400 = 4200).
   - To find this, we locate where the cumulative frequency reaches 4200 on the graph and check the corresponding mark on the x-axis.

3. **Finding the Interquartile Range (IQR)**:
   - The lower quartile (Q1) is at the 25th percentile, corresponding to the 2100th candidate (25% of 8400).
   - The upper quartile (Q3) is at the 75th percentile, corresponding to the 6300th candidate (75% of 8400).
   - To calculate the IQR, we subtract the value of the lower quartile (Q1) from the upper quartile (Q3).

4. **Percentage Passing if the Pass Mark is 38**:
   - We find the cumulative frequency corresponding to the pass mark of 38.
   - The percentage of candidates passing is calculated by taking the number of students who scored 38 or above and dividing it by the total number of candidates (8400), then multiplying by 100.

Let me calculate these values based on the graph you provided:

- **Median**: The cumulative frequency reaches 4200 approximately at a mark of **58**.
- **Interquartile Range (IQR)**: 
   - The 25th percentile (Q1, 2100) is around **43**.
   - The 75th percentile (Q3, 6300) is around **73**.
   - So, the IQR is \(73 - 43 = 30\).
- **Percentage Passing**: At the pass mark of 38, approximately 2000 candidates scored less than 38. So, around \(8400 - 2000 = 6400\) candidates passed. The percentage passing is approximately \(\frac{6400}{8400} \times 100 \approx 76\%\).

Here are the results:
- **Median**: 58
- **Interquartile Range**: 30
- **Percentage Passing**: 76%

Do you have any questions or want further details on these calculations?

### Additional questions:
1. How is the cumulative frequency used to determine the median in such graphs?
2. What other methods can be used to estimate the interquartile range besides the graphical approach?
3. How do you determine the percentile positions from a cumulative frequency curve?
4. What happens if the cumulative frequency graph has irregular steps or flat sections?
5. Can you use the cumulative frequency graph to calculate the mean mark?

### Tip:
Always double-check that your readings from a cumulative frequency graph align with the scale of both axes to ensure accuracy in estimates like the median and quartiles.

In an examination, the marks which 8400 candidates obtained are shown in the cumulative frequency diagram below. The approximate median mark is ____. The approximate interquartile range is ____. If the pass mark is 38, what percentage of the candidates pass? Give your answer to the nearest whole number.

Learn how to analyze a cumulative frequency graph to determine the median, interquartile range, and the percentage of candidates passing an exam. This example uses a graph with 8400 candidates, exploring key mathematical concepts such as the 50th percentile, interquartile range, and pass percentages. Suitable for Grades 9-12.

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