How do you calculate the interquartile range from the following data: 1, 2, 4, 5, 10, 12, 18?

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The interquartile range (IQR) is a measure of statistical dispersion that represents the difference between the third quartile (Q3) and the first quartile (Q1) of a data set. To calculate the IQR for the given data set, follow these steps:

  1. Organize the Data: First, make sure your data is sorted in ascending order. The data set provided is already sorted: 1, 2, 4, 5, 10, 12, 18.
  2. Find Q1 (First Quartile): Q1 is the median of the first half of the data. The first half of the data set is 1, 2, 4, 5. The median of these values (which is the average of 2 and 4) is: Q1 = (2 + 4) / 2 = 3.
  3. Find Q3 (Third Quartile): Q3 is the median of the second half of the data. The second half of the data set is 10, 12, 18. The median of these values is: Q3 = 12.
  4. Calculate the IQR: The IQR is found by subtracting Q1 from Q3: IQR = Q3 - Q1 = 12 - 3 = 9.

Therefore, the interquartile range for the data set 1, 2, 4, 5, 10, 12, 18 is 9.

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