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.