# How do you find the number that corresponds to Quartile 1, when given an even number of scores?

If you have an odd number of data values {39, 40, 42, 44, 47, 48, 49, 51, 53}, what is the score that value that corresponds to Quartile 1? In general, I would like to know if you include the median's value (47) in figuring the position of quartile 1.

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I doubt this convention is universal. For sufficiently large data sets it doesn't really matter anyway. – Qiaochu Yuan Feb 17 '11 at 18:05
I'm teaching this to high school juniors, and I wanted to decide on a convention. The textbooks vary in their methods as well. – kuttaka Feb 17 '11 at 18:09
Depending on your situation, as your students might take the AP Statistics exam at some point in the future, you might want to see if there is some guidance from AP/The College Board as to a preferred definition for medians/quartiles. – Isaac Feb 17 '11 at 18:14

There is no universal agreement on choosing the quartile values.

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### Method 1

1. Use the median to divide the ordered data set into two halves. Do not include the median into the halves.
2. The lower quartile value is the median of the lower half of the data. The upper quartile value is the median of the upper half of the data.

This rule is employed by the TI-83 calculator boxplot and 1-Var Stats functions.

### Method 2

1. Use the median to divide the ordered data set into two halves. Include the median into both halves.
2. The lower quartile value is the median of the lower half of the data. The upper quartile value is the median of the upper half of the data.
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$Q_1$ would be $41$ (i.e. the median of the lower half of the data). One can include the median value or not. You just have to be consistent. I think most calculators do not include the median.

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