Question

Answer the following questions in detail−

From the following data find out D₂, D₇ and D₉

Marks	No of Students
0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100	4 9 14 25 18 6 2 1 1 0

Answer 1

C.I.	fi	C.F.
0–10	4	4
10–20	9	13
20–30	14	27
30–40	25	52
40–50	18	70
50–60	6	76
60–70	2	78
70–80	1	79
80–90	1	80
90–100	0	80
	80

${\mathrm{D}}_2={\left(\frac{2\mathrm{N}}{10}\right)}^{\mathrm{th}}=\left(\frac{160}{10}\right)={16}^{\mathrm{th}}\mathrm{item}$

16^th item falls in 27^th c.f

$$\begin{gathered} {\mathrm{D}}_2=20+\frac{30-20}{14}\left(\frac{160}{10}-13\right)=22.14 \\ {\mathrm{D}}_7={\left(\frac{7\mathrm{N}}{10}\right)}^{\mathrm{th}}={\left(\frac{560}{10}\right)}^{\mathrm{th}}={56}^{\mathrm{th}}\mathrm{item} \end{gathered}$$

56^th item falls in 70^th C.F.

$$\begin{gathered} {\mathrm{D}}_7=40+\frac{50-40}{18}\times \left(\frac{560}{10}-52\right) \\ =42.22 \\ {\mathrm{D}}_9={\left(\frac{9\mathrm{N}}{10}\right)}^{\mathrm{th}}={\left(\frac{720}{10}\right)}^{\mathrm{th}}={72}^{\mathrm{nd}}\mathrm{item} \end{gathered}$$

72^nd item falls in 76^th C.F.

$$\begin{gathered} {\mathrm{D}}_9=50+\frac{60-50}{6}\times \left(\frac{720}{10}-70\right) \\ =53.33 \end{gathered}$$