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Middle/High School Algebra, Geometry, and Statistics (AGS)
9.23 Partition Values for Discrete Variables (Percentiles, Quartiles and Interquartile Range)

Quartiles

Just as one median divides the data into two subgroups, three quartiles divides the data into 4 quarters. The three quartiles are normally represented by the points Q1, Q2, Q3
The lower quartile is denoted by Q1 and the upper quartile by Q3. The second quartile Q2 is the same as the median.

Positions of the Quartile
Lower Quartile Q1 (25 th percentile) : (n+1)/4
Upper Quartile Q3 : 3(n+1)/4

The difference between the upper and the lower quartile value is called the Interquartile range

Example
  • Find Q1, Q3 in the following series.
    33, 32, 55, 47, 21, 50, 27, 12, 68, 49, 40, 17, 44, 48, 62


  • Solution

    Arranging in ascending order, we get
    12, 17, 21, 27, 32, 33, 40, 44, 47, 48, 49, 50, 55, 62, 68

    Here n = 15
    Q1 (25 th percentile) = Size of [(n+1)/4] th item = Size of (15+1)/4 = size of the 4 th item
    So Q1 = 27
    Q3 (75 percentile) = Size of [3(n+1)/4] th item = Size of [3(15+1)]/4 = size of the 12 th item
    So Q3 = 50

    68 = 100 percentile
Q 1: Compute Q1, Q3 for the following frequency distribution if the wages are given only in whole dollars:

Answer:

Q 2: From the data given below calculate the value of 3rd quartile:
2, 3, 4, 7, 8, 9, 10

7
7
10
9

Question 3: This question is available to subscribers only!

Question 4: This question is available to subscribers only!


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