ACT Preparation / Unit 15 ACT 1412 worked example, 60 to 90 seconds
Finding the Median and Quartiles
The idea
The five-number summary is found in four steps. First, order the data. Second, find the median, the middle value or the average of the two middle values. Third, find the first quartile as the median of the lower half and the third quartile as the median of the upper half, leaving the overall median out of both halves when the count is odd. Fourth, record the minimum and the maximum, and compute the IQR.
In practice
Worked example: 12, 7, 15, 9, 20, 11, 14. Ordered: 7, 9, 11, 12, 14, 15, 20. The median is 12. The lower half, 7, 9, 11, has median 9; the upper half, 14, 15, 20, has median 15. The summary is 7, 9, 12, 15, 20, and the IQR is 15 − 9 = 6.
Where people slip
Quartile conventions differ slightly between books and calculators, so use one method consistently. Ordering the data first is never optional.
Your place on the trail
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