Quartiles and Interquartile Range – Practice Problems

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To compute the interquartile range of a given set of data, it is important to first understand the concept of quartile, as the Interquartile range (IQR) is a measure of variability, based on dividing a data set into quartiles. Quartiles divide an ordered data set into four equal parts. The values which divide each part are called the first, second, and third quartiles; they are denoted by Q1, Q2, and Q3, respectively. Q1 is the middle value of the first half of the ordered data set, Q2 is the median value in the set, and Q3 is the middle value in the second half of the ordered data set. The Interquartile Range is (IQR) = Q3 – Q1. This video shows you an example on how to compute the interquartile range.

The following steps are a big help in computing interquartile range:

1. First, arrange the data set into ascending order. For example: 1,3,4,5,5,6,7,7,11,13,15.
2. Next, find the first quartile (Q1) and third quartile (Q3) of the given data set. Q1 is the median or middle value of the first half of the data set while Q3 is the median or middle value of the second half. Given the data set above, the set 1,3,4,5,5 is the first half while 7,7,11,13,15 is the second half. Thus, Q1 = 4 and Q3 = 11. Note that when the data set has two middle values, then get the average of the two numbers in order to get the exact values of the quartiles.
3. Lastly, compute the interquartile range (IQR) by subtracting Q1 from Q3. So for our example we have that IQR = Q3 – Q1 = 11 – 4 = 5.

The interquartile range is used to construct box plots and to find outliers in a data set, thus giving a deeper understanding of the relationship of the data points and the data set as a whole.

Summarize and describe distributions.

CCSS.MATH.CONTENT.6.SP.B.5.C

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Exercises in this Practice Problem
Explain how to find the interquartile range.
Determine the median, the quartiles, and the interquartile range.
Determine the median, the quartiles, and the interquartile range.
Calculate which data points are in which quartile range.
Identify how to find the median.
Determine the median, the quartiles, and the interquartile range.