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The short answer is that that is how the box and whisker plot is to be read. The box and whisker plot is designed to give people a a quick five-point summary of the data set:

1. Minimum value
2. 1st quartile (top 25% or basically the median between the median of the whole data set and the minimum value)
3. Median
4. 3rd quartile (bottom 25% or basically the median between the median of the whole data set and the maximum value)
5. Maximum value
6. Outliers (extreme values if they are really significant)

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x2 is the median. x2 = (27+35)/2= 31

x1 is the first quartile, which is the third value here = 13

x3 is the third quartile, which is the 8th value = 37

x3-x1 is 37-13=24. This is known as the interquartile range, which is the spread of the data around the median.

 

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why is the first quartile the 3rd value? and the third quartile the 8th value?

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The short answer is that that is how the box and whisker plot is to be read. The box and whisker plot is designed to give people a a quick five-point summary of the data set:

1. Minimum value
2. 1st quartile (top 25% or basically the median between the median of the whole data set and the minimum value)
3. Median
4. 3rd quartile (bottom 25% or basically the median between the median of the whole data set and the maximum value)
5. Maximum value
6. Outliers (extreme values if they are really significant)

0 Replies 1 Like ✔Accepted Answer
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