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How To Find Interquartile Range

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How To Find Interquartile Range

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The interquartile range (IQR) is the difference between the third and the first quartiles. It is a measure of dispersion. Quartiles are the values that divide a list of numbers into quarters. Here is how to find the Interquartile Range. 

The interquartile range formula is the first quartile subtracted from the third quartile: 
                                                    IQR = Q_{3}-Q_{1}

How To Find Interquartile Range for an Odd Set of Numbers

  1. Order the numbers from least to greatest.

    Given Data Set: 5, 7, 9, 3, 13, 11, 17, 15, 21, 19, 23

    Order Number: 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23.

  2. Find the median. The median is the data value in the middle of the set. The median in the given data set is 13 since 13 is in the middle of the set.

    Median: 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23

  3. Place the parentheses around the numbers before and after the median. It makes Q1 and Q3 easier to spot.

    (3, 5, 7, 9, 11), 13, (15, 17, 19, 21, 23)

  4. Find the median of both the lower and upper half of the data. Think Q1 as a median in the lower half of the data and Q3 as a median for the upper half of data.

    (3, 5, 7, 9, 11) = 7 = Q1 and (15, 17, 19, 21, 23) = 19 = Q3

  5. Subtract Q1 from Q3 to find the interquartile range

    Q3 – Q1 = 19 – 7 = 12

How To Find Interquartile Range for an Even Set of Numbers

  1. Order the numbers from least to greatest.

    Given Data Set: 42, 51, 62, 47, 38, 50, 54, 43

    Order Number: 38, 42, 43, 47, 50, 51, 54, 62.

  2. Make a mark in the center of the data:

    Median: 38, 42, 43, 47,| 50, 51, 54, 62

  3. Place the parentheses around the numbers before and after the median. It makes Q1 and Q3 easier to spot.

    (38, 42, 43, 47),| (50, 51, 54, 62).

  4. Find the median. We have the even data sets so the median is the average of the middle two numbers.

    (38, 42, 43, 47) = \frac{42+43}{2} = \frac{85}{2} = 42.5 = Q1

    (50, 51, 54, 62) = \frac{51+54}{2} = \frac{105}{2} = 52.5 = Q3

  5. Subtract Q1 from Q3 to find the interquartile range.

    Q3 – Q1 = 52.5 – 42.5 = 10