https://file.aiquickdraw.com/mathbot/file/1727285122176tjz1derm.jpg

From the image you uploaded, we are looking at a cumulative frequency graph showing the lengths of 16 fish, which will allow us to estimate the lower and upper quartiles.

To find the **lower quartile (Q1)** and **upper quartile (Q3)**:
1. **Lower Quartile (Q1)** represents the 25th percentile (i.e., \( \frac{1}{4} \) of the data). Since there are 16 fish, the 25th percentile corresponds to the 4th fish. From the graph, find the length corresponding to a cumulative frequency of 4.
2. **Upper Quartile (Q3)** represents the 75th percentile (i.e., \( \frac{3}{4} \) of the data). For 16 fish, this corresponds to the 12th fish. On the graph, find the length corresponding to a cumulative frequency of 12.

### Estimation based on the graph:
- For the lower quartile (Q1), at the cumulative frequency of 4, the length looks to be approximately **9 inches**.
- For the upper quartile (Q3), at the cumulative frequency of 12, the length seems to be approximately **27 inches**.

Would you like more detailed analysis or further explanations? Let me know if anything is unclear.

### Related questions:
1. How do you calculate the interquartile range from the quartiles?
2. How does cumulative frequency help in interpreting a data set?
3. What is the importance of using quartiles in statistics?
4. How would the graph change if there were more fish measured?
5. How can we estimate the median from this graph?

### Tip:
The interquartile range (IQR) is useful for understanding the spread of the middle 50% of data and can help identify outliers.

Jay measured the lengths of 16 fish. Use the graph below to estimate the lower and upper quartiles of the lengths.

Learn how to estimate the lower and upper quartiles of fish lengths using a cumulative frequency graph. This example shows how to find Q1 and Q3 for 16 fish, with lengths approximately 9 inches for Q1 and 27 inches for Q3. Suitable for students in Grades 9-11.

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