Question

Comment on the performance of the students of three universities given below using weighted mean:

No. of Students are in hundreds

Courses of study	Mumbai		Kolkata		Chennai
	% pass	No. of students	% pass	No. of Students	% pass	No. of Students
M.A	71	3	82	2	81	2
M.COM.	83	4	76	3	76	3.5
B.A	73	5	73	6	74	4.5
B.COM.	74	2	76	7	58	2
B.Sc	65	3	65	3	70	7
M.Sc	66	3	60	7	73	2

Answer 1

Courses	Mumbai			Kolkata			Chennai
	X1	W1	X1W1	X2	W2	X2W2	X3	W3	X3W3
M.A M.Com B.A B.Com B.Sc M.Sc	71 83 73 74 65 66	3 4 5 2 3 3	213 332 365 148 195 198	82 76 73 76 65 60	2 3 6 7 3 7	164 228 438 532 195 420	81 76 74 58 70 73	2 3.5 4.5 2 7 2	162 266 333 116 490 146
		ΣW1 = 20	ΣX1W1 = 1451		ΣW2 = 28	ΣX2W2 = 1977		ΣW3 = 21	ΣX3W3 = 1513

$$\begin{gathered} {\overline{X}}_{W_{\mathit{1}}}=\frac{\Sigma X_1{W}_1}{\Sigma W_1}=\frac{1451}{20}=72.55 \\ {\overline{X}}_{W_{\mathit{2}}}=\frac{\Sigma X_2{W}_2}{\Sigma W_2}=\frac{1977}{28}=70.6 \\ {\overline{X}}_{W_{\mathit{3}}}=\frac{\Sigma X_3{W}_3}{\Sigma W_3}=\frac{1513}{21}=72.04 \end{gathered}$$
Average score of Mumbai is more than Kolkata and Chennai. So performance of Mumbai is better.