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The question asks to estimate the percentage of students who failed the test, given that they needed at least 38% to pass. Based on the cumulative frequency graph, I will guide you through the steps to estimate this:

1. **Identify the cumulative frequency at 38%**:
   From the graph, locate 38% on the x-axis (Test score percentage), and trace upwards to the curve. Then, trace horizontally to the y-axis (Cumulative frequency) to find the corresponding value. 

2. **Estimate the percentage of students who failed**:
   The students who scored below 38% are considered as those who failed. So, take the cumulative frequency value at 38%, and compare it to the total cumulative frequency (which is the highest point on the y-axis, 120 in this case).

3. **Calculation**:
   The percentage of students who failed is calculated as:
   \[
   \text{Percentage who failed} = \frac{\text{Cumulative frequency at 38%}}{\text{Total cumulative frequency}} \times 100
   \]
   From the graph, it seems that the cumulative frequency at 38% is approximately 25. Therefore:
   \[
   \text{Percentage who failed} = \frac{25}{120} \times 100 = 20.83\% \approx 21\%
   \]
   So, around **21% of students** failed the test.

Would you like further details on any step? Here are some related questions you could explore:

1. What is cumulative frequency, and how is it used in data analysis?
2. How can we interpret cumulative frequency graphs to calculate percentiles?
3. What would be the passing percentage if the pass mark was raised to 50%?
4. How can we use cumulative frequency to find the median score of the group?
5. What is the difference between cumulative frequency and frequency distribution?

**Tip**: Cumulative frequency graphs are particularly useful for estimating data quartiles, medians, and percentiles easily by looking at specific points on the curve.

Work out an estimate for the percentage of students that failed the test, given that they needed at least 38% to pass.

Learn how to estimate the percentage of students who failed a test using a cumulative frequency graph. The pass mark is set at 38%, and the graph provides crucial data for calculation. Ideal for students in Grades 9-11.

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