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0,2,6,7,7,7,8,8,8,8,8,9,9,9,10 interquartile range of skewed dataset

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To calculate the interquartile range (IQR) of the given data set \(0, 2, 6, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 10\), follow these steps:

  1. Order the Data:
    The data is already ordered:
    \(0, 2, 6, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 10\)

  2. Find the First Quartile (Q1):
    Q1 is the median of the first half of the data (the lower half). The first half consists of:
    \(0, 2, 6, 7, 7, 7, 8\) (7 values)
    The median of this half is the 4th value, which is 7.

  3. Find the Third Quartile (Q3):
    Q3 is the median of the second half of the data (the upper half). The second half consists of:
    \(8, 8, 8, 8, 9, 9, 10\) (also 7 values)
    The median of this half is the 4th value, which is also 8.

  4. Calculate the Interquartile Range (IQR):
    \(IQR = Q3 - Q1\)
    \(IQR = 8 - 7 = 1\)

Thus, the interquartile range of the dataset is 1.