If the distribution of sales is thought to be symmetric with very little variation, then what may one conclude about the box plot that represents the data set?
A) The whiskers on a box plot the box should be about half as long as the box is wide.
B) The width of the box will be very wide but the whiskers will be very short.
C) The left and right edges will be approximately at equal distance from the second quartile.
D) The width of the box will be very short, but the whiskers will be very long.

Question

Quizplus · Accepted Answer

Since the distribution is symmetric with very little variation, the median (second quartile) should be approximately the center of the distribution, and the left and right edges of the box should be equidistant from it. This means that the box will have moderate width, but the whiskers may be short or long depending on the spread of the data. Option A is incorrect because the ratio of whisker length to box width depends on the spread of the data, not the symmetry. Option B is also incorrect because a very wide box would indicate a distribution with high variability, which is contradictory to the assumption of little variation. Option D is also incorrect because a short box and long whiskers would indicate a skewed distribution, rather than the assumed symmetric distribution.

If the Distribution of Sales Is Thought to Be Symmetric