Q.D for Wheat:

First we need to arrange the observations in the ascending order 

x: 9 10 10 12 15 16 18 19 21 25

Calculation of lower quartile (Q₁):

Q₁ = size of \((\frac{N}{4})^{th}\) item = size of \((\frac{10 + 1}{4})^{th}\) item

= The size of \(\frac{11}{4}^{th}\) item i. e., 2.75^th item

The size of 2.75^th item is size of 2^nd item + 0.75 item Size of 2^nd item = 10

Size of 0.75 item = Size of 3^rd item – 2^nd item = 10 – 10 = 0

Q₁ = size of 2^nd item + 0.75 item is

Q₁ = 10 + 0.75 (10 – 10) = 10 + O.75(0) = 10 + 0

Q₁ = 10

Calculation of Upper Quartile (Q₃):

Q3 = Size of 3 \((\frac{N + 1}{4}^{th})\) item

= Size of \((\frac{3(10 + 1)}{4})^{th}\) item = Size of \((\frac{3(11)}{4})^{th}\) item

= Size of \((\frac{33}{4})^{th}\) item = size of 8.25 item

i.e.. size of 8^th item + 0.25 item (size of 9^th – 8^th item)

Q₃ = 19 + 0.25 (21 – 19) = 19 + 0.25(2)

Q₃= 19 + 0.5

Q₃ = 19.5

Now QD = \(\frac{Q_3 - Q_1}{2} =\) \(\frac{19.5 - 10}{2} =\) \(\frac{9.5}{2} =\) 4.75

QD = 4.75 tonnes