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In the data set below, what is the interquartile range?

1 1 2 3 3 5 5 6 7 8

1 answer

To calculate the interquartile range (IQR), you first need to determine the first quartile (Q1) and third quartile (Q3) of the data set.

The given data set is: 1, 1, 2, 3, 3, 5, 5, 6, 7, 8

  1. Order the data (already ordered): 1, 1, 2, 3, 3, 5, 5, 6, 7, 8

  2. Find Q1 (the median of the first half): The first half of the data (lower half) is: 1, 1, 2, 3, 3 The median of this half (Q1) is the middle value, which is 2.

  3. Find Q3 (the median of the second half): The second half of the data (upper half) is: 5, 5, 6, 7, 8 The median of this half (Q3) is the middle value, which is 6.

  4. Calculate the IQR: IQR = Q3 - Q1 IQR = 6 - 2 = 4

Therefore, the interquartile range is 4.