three distributions, labeled (a), (b), and (c) are represented below by their histograms. each distribution…

three distributions, labeled (a), (b), and (c) are represented below by their histograms. each distribution is symmetrical and is made of 10 measurements. without performing any calculations, order their respective standard deviations $\\sigma_a$, $\\sigma_b$, and $\\sigma_c$.\n\n(a)\n1 2 3 4 5 6 7 8 9 10 11 12 13 14\n\n(b)\n1 2 3 4 5 6 7 8 9 10 11 12 13 14\n\n(c)\n1 2 3 4 5 6 7 8 9 10 11 12 13 14\n\n$\\sigma_{\\square} < \\sigma_{\\square} < \\sigma_{\\square}$

three distributions, labeled (a), (b), and (c) are represented below by their histograms. each distribution is symmetrical and is made of 10 measurements. without performing any calculations, order their respective standard deviations $\\sigma_a$, $\\sigma_b$, and $\\sigma_c$.\n\n(a)\n1 2 3 4 5 6 7 8 9 10 11 12 13 14\n\n(b)\n1 2 3 4 5 6 7 8 9 10 11 12 13 14\n\n(c)\n1 2 3 4 5 6 7 8 9 10 11 12 13 14\n\n$\\sigma_{\\square} < \\sigma_{\\square} < \\sigma_{\\square}$

Answer

That looks like a stats problem about understanding standard deviation!

Basically, the main takeaway here is how "spread out" the data is from the center. When you're looking at these histograms, you're just trying to eyeball which one has more of its data points further away from the middle. The more spread out the boxes are, the higher the standard deviation.

It's one of those concepts that feels a bit abstract until you start visualizing it like this. Does that way of thinking about "spread" make sense to you, or does it still feel a bit fuzzy?