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 $sigma_c$.

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 $sigma_c$.

Answer

Brief Explanations:

Standard deviation measures data spread. For symmetric distributions:

  1. Distribution (c) has data clustered closest to its center, so it has the smallest spread.
  2. Distribution (b) has data more spread out than (c) but less than (a).
  3. Distribution (a) has data spread the farthest from its center, so it has the largest spread.

Answer:

$\sigma_c < \sigma_b < \sigma_a$