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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$\begingroup$$\endgroup$ $\begingroup$There is no universal agreement on choosing the quartile values.
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Method 1
- Use the median to divide the ordered data set into two halves. Do not include the median into the halves.
- 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
- Use the median to divide the ordered data set into two halves. Include the median into both halves.
- 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.
$Q_1$ 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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