Question

Following are the marks obtained by two students: Mollie and Isha, in 10 sets of examinations:

Marks of obtained by Mollie	44	80	76	48	52	72	68	56	60	54
Marks of obtained by Isha	48	75	54	60	63	69	72	51	57	66

Out of Mollie and Isha, who is more consistent?

Answer 1

Mollie			Isha
XM	${\mathit{x}}_{\mathbf{M}}\mathbf{=}{\mathit{X}}_{\mathbf{M}}\mathbf{-}{\overline{\mathit{X}}}_{\mathit{M}}$	${\mathit{x}}_{\mathbf{M}}^{\mathbf{2}}$	XI	${\mathit{x}}_{\mathbf{I}}\mathbf{=}{\mathit{X}}_{\mathbf{I}}\mathbf{-}{\overline{\mathit{X}}}_{\mathit{I}}$	${\mathit{x}}_{\mathit{I}}^{\mathbf{2}}$
44	−17	289	48	−13.5	182.25
80	19	361	75	13.5	182.25
76	15	225	54	−7.5	56.25
48	−13	169	60	−1.5	2.25
52	−9	81	63	1.5	2.25
72	11	121	69	7.5	56.25
68	7	49	72	10.5	110.25
56	−5	25	51	−10.5	110.25
60	−1	1	57	−4.5	20.25
54	−7	49	66	4.5	20.25
ΣXM=610		$\mathrm{\Sigma }{x}_{\mathrm{M}}^2=1370$	ΣXI=615		$\mathrm{\Sigma }{x}_{\mathrm{I}}^2=742.5$

$$\begin{gathered} {\overline{X}}_M=\frac{\Sigma X_M}{N}=\frac{610}{10}=61marks \\ {\sigma }_M=\sqrt{\frac{{\mathrm{\Sigma x}}_{\mathrm{M}}^2}{\mathrm{N}}}=\sqrt{\frac{1370}{10}}=\sqrt{137}=11.70 \\ \mathrm{C}.\mathrm{V}\mathrm{of}\mathrm{Mollie}\text{'}\mathrm{s}\mathrm{marks}=\frac{{\sigma }_M}{\overline{X_M}}\times 100=\frac{11.70}{61}\times 100=19.18\% \end{gathered}$$


$$\begin{gathered} {\overline{X}}_I=\frac{\Sigma X_I}{N}=\frac{615}{10}=61.5 \\ {\sigma }_I=\sqrt{\frac{\Sigma x_I^2}{N}}=\sqrt{\frac{742.5}{10}}=\sqrt{74.25}=8.62 \\ \mathrm{C}.\mathrm{V}\mathrm{of}\mathrm{Isha}\text{'}smarks=\frac{\sigma }{\overline{X}}\times 100=\frac{8.62}{61.5}\times 100=14.01\% \end{gathered}$$

Isha is more consistent in securing makes as her C.V. (14.01)% is less than that of Mollie's C.V. (19.18)%