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How-Tos / Math
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How To Find Interquartile Range

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How To Find Interquartile Range +
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Image Credits: Pinterest.

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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. 

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

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How To Find Interquartile Range for + an Odd Set of Numbers

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  1. Order the numbers from least to greatest.

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

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

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    2. +
  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

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  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) +

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  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 +

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  5. Subtract Q1 from Q3 to find the interquartile range

    Q3 – Q1 = 19 – 7 = + 12

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    6. +
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How To Find Interquartile Range + for an Even Set of Numbers

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  1. Order the numbers from least to greatest.

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

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

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

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

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    3. +
  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).

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    4. +
  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 +

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

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

    Q3 – Q1 = 52.5 – + 42.5 = 10

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