Question

Given the following data set, find the Quartiles:  {1, 1, 4, 5, 6, 6, 7, 8, 10, 11, 13, 14, 15, 16}

Answer 1

Here, Data arranged in Ascending order.

Then,

We find out Quartiles..

Q_k = size of {k * (n+1)/4}^th item. ...........Where, k = 1,2,3

First Quartile = Q1 =

Q₁ = size of {1 * (14+1)/4}^th item.

Q₁ = size of {3.75}^th item.

Q₁ = size of {3}^rd item + 0.75 * (size of 4^th item - size of 3^rd item)

Q₁ = 4 + 0.75 * (5-4)

Q₁ = 4.75

Find: Second Quartile = Q2 =  Median:

Median = size of {(n+1)/2}^th item.

Q₂ = size of ({14+1)/2}^th item.

Q₂ = size of {7.5}^th item.

Q₂ = size of {7}^th item + 0.5 * (size of 8^th item - size of 7^th item)

Q₂ = 7 + 0.5 * (8-7)

Q₂ = Median = 7.5

Third Quartile: Q₃ =

Q_k = size of {k * (n+1)/4}^th item.

Q₃ = size of {3 * (14+1)/4}^th item.

Q₃ = size of {11.25}^th item.

Q₃ = size of {11}^th item + 0.25 * (size of 12^th item - size of 11^th item)

Q₃ = 13 + 0.25 * (14-13)

Q₃ = 13.25