Quartiles Quartiles | Mathematics for Grade 10 PDF Download

Quartile Formula

What Is Quartile Formula? 

• First Quartile(Q1) = ((n + 1)/4)th Term 
• Second Quartile(Q2) = ((n + 1)/2)th Term
• Third Quartile(Q3) = (3(n + 1)/4)th Term
  

1st quartile is also known as the lower quartile. 2nd quartile is the same as the median dividing data into 2 equal parts. 3rd quartile is also called the upper quartile.
The interquartile range is calculated as Upper Quartile – Lower Quartile.

Solved Example

Arranging the values in ascending order: 19, 20, 21, 22, 23, 24, 25, 26, 27
Putting the values in the formulas above we get,
Median(Q2) = 5th Term = 23
Lower Quartile (Q1) = Mean of 2nd and 3rd term = (20 + 21)/2 = 20.5
Upper Quartile(Q3) = Mean of 7th and 8th term = (25 + 26)/2 = 25.5
IQR = Upper Quartile−Lower Quartile
IQR = 25.5 – 20.5
IQR = 5

Example 2: What will be the upper quartile for the following set of numbers?
26, 19, 5, 7, 6, 9, 16, 12, 18, 2, 1.

The formula for the upper quartile formula is Q3 = ¾(n + 1)th Term.
The formula instead of giving the value for the upper quartile gives us the place. For example, 8th place, 10th place, etc.
So firstly we put your numbers in ascending order: 1, 2, 5, 6, 7, 9, 12, 16, 18, 19, 26. There are a total of 11 numbers, so:
Q3 = ¾(n + 1)th Term.
Q3 = ¾(12)th Term. = 9th Term.
The upper quartile (18) is the 9th term or on the 9th place from the left.

Example 3: Find the 3rd quartile in the following data set: 4, 5, 8, 7, 11, 9, 9

Let us first arrange our array in ascending order and it becomes 4, 5, 7, 8, 9, 9, 11
The median of our data is 8.
In order to find the 3rd quartile, we have to deal with the data points that are greater than the median that is 9, 9, 10.
In order to find the 3rd quartile, we have to find the median of the data points that are greater than the median that is 9, 9, 10.