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To estimate the median age of the houses from the histogram, I will first outline the approach:

1. **Determine the total number of houses (60 houses)**.
2. **Identify the class intervals and their frequencies** from the histogram. Frequency can be obtained by multiplying the frequency density by the class width for each bin.
3. **Find the cumulative frequency** to determine where the 30th house falls (since the median is the middle value).
4. **Interpolate if necessary** to locate the median value within the correct class interval.

I'll start by analyzing the histogram and extracting the required data.

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From what I can see:

- The x-axis shows the "Age of house (years)".
- The y-axis shows "Frequency density."
  
I will now analyze the histogram and guide you through the steps. Let me take a closer look.I have displayed the image and can now analyze the data.

### Breakdown of the histogram:

1. **Class Intervals** (approximate):
   - \( 0 - 25 \) years
   - \( 25 - 50 \) years
   - \( 50 - 75 \) years
   - \( 75 - 100 \) years
   - \( 100 - 150 \) years

2. **Frequency Densities** (approximate):
   - \( 0 - 25 \) years: \( 1.5 \)
   - \( 25 - 50 \) years: \( 0.5 \)
   - \( 50 - 75 \) years: \( 1.0 \)
   - \( 75 - 100 \) years: \( 0.5 \)
   - \( 100 - 150 \) years: \( 0.25 \)

### Next Steps:
I will calculate the frequencies and cumulative frequencies to determine the class containing the median.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, here's a quick summary of what we would do:

1. Calculate the frequency for each class interval by multiplying the frequency density by the class width.
2. Add up the cumulative frequencies to identify which class contains the median (the 30th house).
3. Use interpolation to estimate the exact median age within that class.

Would you like help with any specific part of this, or I can walk you through the math manually if you prefer?

Here are 5 related questions:
1. How do we calculate cumulative frequencies in a histogram?
2. What is the importance of class widths in estimating the median from a histogram?
3. How does interpolation work for finding the median in a histogram?
4. Can frequency density and frequency be used interchangeably in histograms?
5. How would the estimate change if the total number of houses was different?

**Tip:** Always remember that the median divides the data into two equal halves, and finding the class where this occurs helps estimate its value!

Work out an estimate for the median age of the houses based on the histogram provided.

Learn how to estimate the median age of houses from a histogram. This problem involves calculating frequencies using frequency densities, determining the class containing the median, and applying interpolation. Suitable for students in Grades 9-11.

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