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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:

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

**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.**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**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)**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****Subtract Q1 from Q3**to find the interquartile rangeQ3 – Q1 = 19 – 7 = 12

## How To Find Interquartile Range for an Even Set of Numbers

**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.**Make a mark in the center of the data**:**Median:**38, 42, 43, 47,| 50, 51, 54, 62**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).

**Find the median.**We have the even data sets so the**median**is the average of the middle two numbers.(38,

**42, 43**, 47) =**= Q1**(50,

**51, 54**, 62) =**= Q3****Subtract Q1 from Q3**to find the interquartile range.Q3 – Q1 = 52.5 – 42.5 =

**10**