https://file.aiquickdraw.com/mathbot/file/1728190705426lv9ddujk.jpg

The image shows a histogram representing the distribution of total returns for 1,528 common stocks listed on the New York Stock Exchange (NYSE) in one year. The returns are expressed as a percentage of the beginning price, and the task is to approximate the smallest and largest total returns.

### Observations from the Histogram:
- The x-axis represents the **Percentage Total Return**, ranging from -60% to 100%.
- The y-axis shows the **Percentage of NYSE Stocks** in each return range.
- Most stocks have returns clustered between 0% and 40%, with a peak around 20%.
- The distribution appears slightly skewed to the right, with a small number of stocks having returns as high as 80% to 100%.

### Answering the Question:
The task asks for the approximate smallest and largest total returns.

- **Smallest Total Return**: Based on the left tail of the distribution, the lowest value where bars appear is around **-25%**.
- **Largest Total Return**: The highest value on the right where the bars end is around **75%**.

These numbers match the pre-filled answers in the image.

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Would you like further details on interpreting histograms or variability in distributions? Here are five related questions for deeper understanding:

1. How can you determine the mean and median of a distribution from a histogram?
2. What does skewness in a histogram tell you about stock returns?
3. How would you calculate the range of this distribution?
4. What are the outliers in this histogram, and how might they affect analysis?
5. How could you use this histogram to estimate the standard deviation of stock returns?

**Tip**: When interpreting histograms, the width of each bin represents an interval of data, while the height shows the frequency (or percentage) of observations within that interval.

Based on the histogram showing the total returns of 1,528 NYSE stocks in a year, what are the approximate smallest and largest total returns?

This problem involves analyzing a histogram showing the total returns of 1,528 NYSE stocks in a year. The task is to determine the smallest and largest total returns based on the distribution, which represents the variability in stock performance. A detailed breakdown of the histogram's data is provided for high school-level students.

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