Statistics: Box Plots?

Hi,

I'll really appreciate it if someone could help me with interpreting box plots. The web has helped, but I am still a little bit confused.


#1. Which one of the 3 distributions is most likely to have a mean that is greater than
the median? A B C I think it's C. The box plot is shifted most to the left.
#2. Which one has the smallest maximum? A B C Would the answer be A?
#3. Which one has the smallest value of Q3? A B C B?

Thank you

Illeana said:

#1. Which one of the 3 distributions is most likely to have a mean that is greater than the median?

I think it's C. The box plot is shifted most to the left.

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I'm sorry but I have no idea what you mean by "shifted most to the left". (The plots, in this case, are top-to-bottom, not left-to-right, and the plot for C is the right-most one.) Please reply with clarification.

When you reply, please include your understanding of "mean" and "median", especially as they relate to box-plots and outliers.

Illeana said:

#2. Which one has the smallest maximum? A B C

Would the answer be A?

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While the upper whisker for B appears to be a tad lower than that for A, B's outliers raise its maximum. Your answer is correct.

Illeana said:

#3. Which one has the smallest value of Q3? A B C

B?

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The upper edge of the reddish boxes represent Q3. The upper edge of B's box is the lowest. Your answer is correct.

As far as I know, the horizontal line (white line) in the box would be the median. I am not sure how to determine the mean, because it really only gives you values of the first quartile, median and third quartile. Do tell me if I am wrong.

For the first question, what I was trying to say is that it seems the median is closer to the left line of the box in the box plot. And that's why it looks like 'C' has a mean greater than the median. This might be completely wrong though, so I'll appreciate a good explanation.

Thank you!

Illeana said:

As far as I know, the horizontal line (white line) in the box would be the median. I am not sure how to determine the mean, because it really only gives you values of the first quartile, median and third quartile. Do tell me if I am wrong.

Click to expand...

Check the definitions of median (re: box plots) and means, especially with respect to outliers.

Illeana said:

For the first question, what I was trying to say is that it seems the median is closer to the left line of the box in the box plot.

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The median is an horizontal line crossing the entire box. There is no "closer" to either "side"; the line crosses the entire box and intersects each side of the box.