Quartile Formula

What is Quartile Formula?

A quartile is defined as a statistical term which disintegrates the given data into 4 quarters. Basically, quartile divides provided points of data into a set of 4 quarters in the number line.

Remember that the data points are random. You need to plot the numbers in the number line first. This has to be done in ascending order after which you have to break them into quartiles. Eventually one can conclude that it is an extended edition of the median.

Once the data is divided, we have:

• First quartile: Also called the lower quartile. It sets aside the lowest 25% of data from the rest of 75%

• Second quartile: You may refer to this as the middle quartile. This expresses the numbers as 2 equal parts

• Third quartile: This separates the uppermost 25% of given data from the rest 75%

What is the quartile formula in mathematical terms?

When we arrange set of observations in ascending order, mathematical representation of quartiles look like this:

Q₁ (first quartile) = [(n+1)/4]^th term

Q₂ (second quartile) = [(n+1)/2]^th term

Q₃ (third quartile) = [3(n+1)/4]^th term

We may calculate the interquartile range by finding: Q₃ – Q₁

Also see:

Solved Examples

1. Determine the median, first quartile, third quartile and also the interquartile range for the given data set: 34, 36, 38, 35, 38, 43, 41, 40, 47.

Solution: At the beginning, you need to arrange the data in ascending order.

It will be: 34, 35, 36, 38, 38, 40, 41, 43, 47

Incorporating the values within the above-mentioned formulas we get,

Q₂ or median = 38

First quartile = [(n+1)/4]^th term or, (9+1)/4^th term = 2.5^th term = 35.5

Third quartile = [3(n+1)/4]^th term or, [3(9+1)/4]^th term = 7.5^th term = 42

Interquartile range = Q₃ – Q₁ = 42 – 35.5 = 6.5

Answer: Q₂ = 38, Q₁ = 35.5, Q₃ = 42, IQR = 6.5

2. Determine the third quartile.

Data set: 31, 23, 9, 11, 10, 13, 19, 17, 22, 6, 3

Solution: Formula we have learnt for upper or third quartile is: [3(n+1)/4]^th term.

This formula guides you to the position of the third quartile. It does not reveal the value.

Let us first arrange the numbers: 3, 6, 9, 10, 11, 13, 17, 19, 22, 23, 31.

For large data sets, we recommend you use the spreadsheet to arrange your data. Here, we have 11 numbers.

Third quartile = ¾(n+1)^th term = ¾(11+1)^th term = 9^th term

Answer: Q₃ = 22.

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