https://file.aiquickdraw.com/mathbot/file/17261839532335qgy3bjz.jpg

To calculate the **mean**, **median**, and **mode** from the histogram, I'll first extract the data points represented by the histogram. Here's the data from the image based on the X-axis intervals and the Y-axis values (frequencies):

- **0-10**: 0
- **11-20**: 3
- **21-30**: 1
- **31-40**: 17
- **41-50**: 2
- **51-60**: 7

### 1. **Mean**
The mean can be calculated by treating the midpoint of each interval as a representative value for the entire interval. The midpoint for each class is as follows:

- **0-10**: midpoint = 5
- **11-20**: midpoint = 15
- **21-30**: midpoint = 25
- **31-40**: midpoint = 35
- **41-50**: midpoint = 45
- **51-60**: midpoint = 55

The formula for the mean is:

\[
\text{Mean} = \frac{\sum (f \times x)}{\sum f}
\]

Where:
- \( f \) is the frequency (Y-axis values)
- \( x \) is the midpoint of each class

Let me calculate the mean.The **mean** of the data is 38.0.

### 2. **Median**
The median is the value that divides the dataset into two equal halves. To find the median, we need to look at the cumulative frequencies to determine which class contains the median.

Here are the cumulative frequencies:
- **0-10**: 0
- **11-20**: 3
- **21-30**: 4
- **31-40**: 21
- **41-50**: 23
- **51-60**: 30

Since there are 30 data points in total, the median will be the value corresponding to the 15th and 16th data points (since the total frequency is even, the median is the average of the two middle points).

From the cumulative frequencies, we can see that the 15th and 16th points fall in the **31-40** interval. Hence, the median lies in this interval, which has a midpoint of 35.

### 3. **Mode**
The mode is the class with the highest frequency. From the data, the class **31-40** has the highest frequency (17), so the mode is the midpoint of this class, which is **35**.

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### Summary:
- **Mean**: 38.0
- **Median**: 35 (falls within the 31-40 class)
- **Mode**: 35 (most frequent class is 31-40)

Would you like more details or have any further questions?

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Here are 5 follow-up questions you might consider:
1. How is the spread of the data affecting the median compared to the mean?
2. What would happen if you added more data points in the 21-30 range?
3. How would you calculate the variance and standard deviation for this dataset?
4. Could the mean be affected significantly if the highest or lowest class frequencies change?
5. Why is the mode particularly useful when looking at this type of histogram?

**Tip**: When calculating the median for grouped data, the cumulative frequency helps locate the exact interval in which the median lies.

Learn how to determine the mean, median, and mode from a histogram using the midpoints and frequencies from the data. This solution includes a step-by-step breakdown with relevant formulas and statistics concepts. Suitable for students in Grades 9-12.

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