# Find the 3 quartiles in the following data set: 4 5 8 7 11 9 9.

**Solution:**

A quartile divides data into three points:

- Lower quartile(Q₁)
- Median(Q₂)
- Upper Quartile(Q₃)

To find the 3 quartiles, arrange the data points in ascending order. 4 5 7 8 9 9 11.

Here n = number of data points given = 7

Lower Quartile formula is the (n+1)/4^{th} term

= (7 + 1)/4 = 2^{nd }term of the series

The second term of the given series is 5. Hence the **lower quartile is 5**.

The next quartile is actually the median and that is the (n+1)/2^{th} term or Q₁

The middle quartile or the median (Q₂) = (7 + 1)/2 = 4^{th} term

The fourth term of the series is 8. Hence the **middle quartile is 8**.

The Upper quartile is the 3(n+1)/4^{th} term or Q₃

The 3(n+1)/4^{th} term = 3(7 + 1)/4 = 6 ^{th} term of the series.

The sixth term of the series is 9. Hence the **upper quartile is 9**.

Thus the three quartiles Q₁, Q₂ and Q₃ are 5, 8 and 9 respectively.

## Find the 3 quartiles in the following data set: 4 5 8 7 11 9 9.

**Summary:**

The three quartiles are basically positional identities of a given series of numbers. The three quartiles of the given number series i.e. 4 5 8 7 11 9 9 are Q₁ = 5; Q₂ = 8 and Q₃ = 9.