Calculate the first quartile from the data given below.

Preparing a cumulative frequency table from the given data, we get.

By formula,

First quartile (Q₁) = The value of \((\frac N4)^{th}\) item

=The value of \((\frac{45}4)^{th}\) item

= The value of 11.25^th item.

Here, C.F just greater than 11.25 is 20 and it lies in the class (10 - 15).

Therefore, First quartile class = (10 - 15)

Again, by formula

First quartile (Q₁) = \(L\;+\;(\frac{{\displaystyle\frac N4}-c.f}f)\times i\)

Where, L = 10, \(\frac N4\) = 11.25, c.f = 6, f = 14, i = 5

Therefore, Q₁ = 10 + \(10\;+\;(\frac{11.25\;-\;6}{14})\times5\)

= \(10+\frac{5.25}{14}\times5\)

= 10 + 1.88

First quartile (Q₁) = 11.88