Quartiles Given Frequency Distributions

In this class, We discuss Quartiles Given Frequency Distributions.

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The reader should have prior knowledge of quartiles and their uses. Click Here.

For continuous interval frequency distribution

Q1 = L + (h/f)((N/4)-c) lower quartile

Q2 = L + (h/f)((N/2)-c) median quartile

Q3 = L + (h/f)(3(N/4)-c) upper quartile

The above-median quartile equation is explained when we discussed the median for frequency distribution.

Example:

Eight coins are tossed together at random. 

The number of heads is recorded.

The experiment was repeated 256 times, and the frequency for showing the head is in the table.

Find the quartile points.

N = 256

Q1 = N/4 = 64

Q2 = N/2 = 128

Q3 = 3N/4 = 192

The lower quartile value is three because 64 comes to X value 3.

The median quartile value is four because 128 comes to an X value of 4.

The upper quartile value is five because 192 comes to an X value of 5.

Example 2: Continuous class

The below table shows the data distribution.

N/4 = 50/4 = 12.5 = 13

Q1 = class 20 – 30

N/2 = 50/2 = 25

Q2 = class 30 – 40

3N/4 = 150/4 = 37.5 = 38

Q3 = class 40 – 50.

The quartile value should be a value between the lower and upper values of the class.

Q1 = L + (h/f)((N/4)-c) lower quartile

Q1 = 20 + (10/8)(12.5 – 11)

Q1 = 21.8

The reader can do the remaining quartile points.