Is the lower quartile here 18.5 or 27 ? Take the following list of data: 4 <mte

Lucille Cummings

Lucille Cummings

Answered question

2022-06-26

Is the lower quartile here 18.5 or 27?
Take the following list of data:
4   10   27   27   29   34   34   34   37
If I remove the median which is 29 then the left hand side is:
4   10   27   27
The median of this side is 10 + 27 2 = 18.5
But if I use the percentile formula:
P 25 = 25 100 9 = 2.25
2.25 is not a whole number so we take the next whole number which is 3
The P 25 is the third value which is 27
Note: Wikipedia defines the lower quartile as the middle number between the lowest number and the median. In this case it would be 27
Which of these is the lower quartile, 18.5, 27, or somethings else?

Answer & Explanation

seraphinod

seraphinod

Beginner2022-06-27Added 22 answers

The lower quartile of that data set is 10 + 27 2 = 18.5. The lower quartile is essentially the median of the lower half of the data set. Calculating the lower quartile is no different when the lower half of the data set has an even number of data points than if it you were calculating the median: average the middle two.

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