Question

Answer the following questions in detail−

Find D₃ and D₄ from the following data.

Marks	1	2	3	4	5	6
No. of Students	5	6	4	5	10	15

Answer 1

X	f	C.F.
1	5	5
2	6	11
3	4	15
4	5	20
5	10	30
6	15	45
	45

$$\begin{gathered} {\mathrm{D}}_3=3{\left(\frac{\mathrm{N}+1}{10}\right)}^{\mathrm{th}}\mathrm{item} \\ =3\left(\frac{45+1}{10}\right)=13.8^{\mathrm{th}}\mathrm{item} \end{gathered}$$

13.8^th item falls in 5^th C.F which corresponds to X equal to 1

Thus, D₃ = 1

$$\begin{gathered} {\mathrm{D}}_4=4+{\left(\frac{\mathrm{N}+1}{10}\right)}^{\mathrm{th}}\mathrm{item} \\ =4{\left(\frac{45+1}{10}\right)}^{\mathrm{th}}=18.4^{\mathrm{th}}\mathrm{item} \end{gathered}$$

18.4^th item falls in 20^th C.F. which corresponds to X equal to 4

Thus, D₄ = 4