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Interquartile Range Calculator

Quartiles and the interquartile range from any list: the data is ordered, the quartile positions are calculated with the n plus one rule, and the IQR falls out as upper minus lower. The IQR matters because it ignores extremes, which is why exams love asking about it.

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    Worked Example

    Find the quartiles and IQR of 2, 4, 5, 7, 8, 9, 11.

    1. The 7 numbers are already in order
    2. Positions with the (n + 1) rule: Q1 at position 2, Q2 at 4, Q3 at 6
    3. Read off:Q1 = 4, median = 7, Q3 = 9
    4. IQR = 9 − 4 = 5

    Answer: Q1 4, median 7, Q3 9, IQR 5

    Try These Yourself

    A data set has Q1 = 12 and Q3 = 31. What is the IQR?Show answerHide answer

    Answer: 19

    31 − 12.

    For 11 ordered values, which position is Q3?Show answerHide answer

    Answer: 9th

    3 × (11 + 1) ÷ 4 = 9.

    Why prefer the IQR over the range?Show answerHide answer

    Answer: It ignores extreme values

    It only spans the middle half of the data.