The problem asks you to compare the standard deviations of three distributions, shown by their histograms. Here's the key approach:

• Standard deviation measures the spread or dispersion of the data around the mean. A higher spread means a larger standard deviation.

Looking at the histograms:

1. Histogram (a): The data is more concentrated in the center with fewer values at the extremes. This should have the smallest spread and hence the smallest standard deviation.
2. Histogram (b): The data is more spread out, with values at the extremes and some in the middle. This suggests the highest standard deviation since the data points are more dispersed.
3. Histogram (c): This distribution is in-between (a) and (b). The data is still centered but a bit more spread out than (a). Thus, its standard deviation will be greater than (a) but less than (b).

Order of standard deviations:

$\sigma_a < \sigma_c < \sigma_b$

Would you like a more detailed explanation? Here are 5 questions for further exploration:

1. What is the exact formula for standard deviation and how is it calculated?
2. How does symmetry in a distribution affect the standard deviation?
3. Why is it important that all histograms have the same number of measurements in this problem?
4. What other properties of a distribution, besides spread, influence the standard deviation?
5. How would adding more measurements to the histograms impact their standard deviations?

Tip: Visual comparison of histograms focuses on spread and outliers. More spread leads to higher standard deviation.