https://file.aiquickdraw.com/mathbot/file/1726457066359qfv14fn3.jpg

To solve this problem, let's analyze the given histograms and estimate their standard deviations without calculations.

The key idea is that the standard deviation measures the spread of the data. A greater spread means a higher standard deviation, while a smaller spread (data closer to the mean) means a lower standard deviation.

### Histogram Analysis:
- **Histogram (a)**: The data is fairly spread out, with values ranging from about 3 to 12. It has moderate variability.
- **Histogram (b)**: This distribution appears more spread out than (a), with values ranging from about 1 to 14. It has a wider spread and likely the highest standard deviation.
- **Histogram (c)**: The data in (c) is tightly clustered between values of around 5 and 9. The spread is minimal, so this should have the smallest standard deviation.

### Ordering of Standard Deviations:
From the analysis, the order of standard deviations from smallest to largest should be:
\[
\sigma_c < \sigma_a < \sigma_b
\]

Would you like a more detailed explanation of standard deviation or further clarifications? Here are some related questions for additional practice:

1. What is the mathematical formula for standard deviation?
2. How do you interpret the standard deviation in real-world scenarios?
3. Can a symmetric distribution have a skewed standard deviation?
4. What are the factors that can affect the spread of a dataset?
5. How would the presence of outliers affect the standard deviation of a dataset?

**Tip:** Always remember that a tighter concentration of data points around the mean results in a smaller standard deviation.

Three distributions, labeled (a), (b), and (c), are represented by histograms. Without performing any calculations, order their respective standard deviations: σa, σb, and σc.

Analyze three symmetric histograms to determine the order of standard deviations. This exercise helps understand how data spread influences standard deviation without requiring complex calculations. Suitable for Grades 9-12 statistics students.

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