Solved Problems on Quartile Formula

Problem 1: Find Quartile 1 for the given data 10, 30, 5, 12, 20, 40, 25, 15, 18.

Solution:

Step 1: Sort the given data in ny order ( ascending order / descending order) 

5, 10, 12, 15, 18, 20, 25, 30, 40

Step 2: Find 1st Quartile

FIrst Quartile [Tex]= (\frac{n + 1}{4})^{th}           [/Tex] term

Here n = 9 because there are total 9 numbers in the given data.

⇒ First Quartile = ((9 + 1)/4)^th term

⇒ First Quartile = (10/4)^th term

⇒ First Quartile = 2.5^th term

Now, 2.5^th term = 2nd term + (0.5) (3^rd term – 2^nd term)

⇒ 2.5^th term = (10) + (0.5) (12 – 10)

⇒ 2.5^th term = 10+1 

⇒ 2.5^th term = 11

The First Quartile value is 11.

Problem 2: Find the Second Quartile for the data 10, 30, 5, 12, 20, 40, 25, 15, 18.

Solution:

Step 1: Sort the given data in the ascending order

5, 10, 12, 15, 18, 20, 25, 30, 40

Step 2: Find 2nd Quartile

Second Quartile [Tex]= (\frac{n + 1}{2})^{th}           [/Tex] term

Here n = 9 because there are total 9 numbers in the given data.

⇒ Second Quartile [Tex]= (\frac{9 + 1}{2})^{th}           [/Tex] term

⇒ Second Quartile = (10/2)^th term

⇒ Second Quartile = 5^th term

5^th term is 18

So the Second Quartile value is 18.

Problem 3: Find the third Quartile for the data 10, 30, 5, 12, 20, 40, 25, 15, 18.

Solution:

Step 1: Sort the given data in the ascending order

5, 10, 12, 15, 18, 20, 25, 30, 40

Step 2: Find 3^rd Quartile

Third Quartile [Tex]= \frac{3(n + 1)}{4}^{th}    [/Tex] term

Here n = 9 because there are total 9 numbers in the given data.

⇒ Third Quartile [Tex]= \frac{3(n + 1)}{4}^{th}     [/Tex] term

⇒ Third Quartile= [Tex]\frac{3 \times (10)}{4}^{th}     [/Tex] term

⇒ Third Quartile= 7.5^th term

7.5^th term is average result of 7^th and 8^th term = (25 + 30)/2 = 27.5

Remember:  7.5^th term = 7^th term + (0.5) (8^th term – 7^th term)

The most recommended method to find value is mentioned above

Because the term not always N.5 something  it may vary from N.1 to N.9 

Here, N be any natural number.

So the third Quartile value is 27.5.

Problem 4: Find the first, second, and third Quartile  for the data 8, 5,15,  20, 18, 30,  40, 25

Solution:

Step 1: Sort the given data in the ascending order

5, 8, 15, 18, 20, 25, 30, 40.

Step 2: Find all Quartiles step by step

First Quartile= {(n + 1)/4}^th term

Here n = 8 because there are total 8 numbers in the given data.

⇒ First Quartile = {(8 + 1)/4}^th term

⇒ First Quartile= {9/4})^th term

⇒ First Quartile= 2.25^th term

Thus, 2.25^th Term  = 2nd term + (0.25)(3^rd term – 2^nd term )

⇒ 2.25^th Term = 8+(0.25)(15-8) = 9.75

First Quartile value is 9.75

Second Quartile = {(n + 1)/2}^th term

⇒ Second Quartile = (9 + 1)/2}^th term

⇒ Second Quartile = {10/2}^th term

⇒ Second Quartile = 5^th term

5^th term is 20

So the second Quartile value is 20.

Third Quartile = 3(n + 1)/4^th term

⇒ Third Quartile = (3(8 + 1)/4)^th term

⇒ Third Quartile = (27/4)^th term

⇒ Third Quartile = 6.75^th term

Thus, 6.75^th  = 6th term +(0.75)(7th -6th)

⇒ 6.75^th = 25+ (0.75)(5)= 28.75

So the third Quartile value is 28.75

Problem 5: What is the Interquartile Range for the data if the first quartile is 10 and the third quartile is 30cm?

Solution:

Given,

• Q₁ = 10
• Q₃ = 30

Interquartile range = Q₃ – Q₁

⇒ Interquartile range = 30 – 10

Thus, Interquartile range is 20.

Problem 6: What is the Quartile Deviation for the data if the first quartile is 15 and the third quartile is 30cm?

Solution:

Given,

• Q₁ = 15
• Q₃ = 30

Quartile Deviation = (Q₃ – Q₁)/2

⇒ Quartile Deviation = (30 – 15)/2

⇒ Quartile Deviation = 15/2

Thus, Quartile Deviation is 7.5

Quartiles are the set of values that divide the data points into four identical values using three individual data points. Thus, a quartile is a very important topic in Statistics that helps us to study large amounts of data, they are used to divide the large data values into four equal quarters. These quartiles show the data that is near the middle points of the large data set.

In this article, we will learn about the quartiles as well as the formulas for the first quartile, second quartile, and third quartile and also provide a step-by-step guide to help you easily calculate quartiles. So, let’s start with the definition of quartile first.