salary(in lakh per annum) no of employees in no of employees in less than organization 1...

salary(in lakh per annum)	no of employees in	no of employees in
less than	organization 1	organization 2
5	655	950
10	872	1657
15	1033	2108
20	1144	2488
25	1189	2645
30	1204	2769
35	1212	2825
40	1217	2858
45	1220	2870
50	1222	2877
55	1224	2882
60	1225	2885
65		2888
70		2890

from the above data please find the mean,variance,standrad deviation and coefficient of variation

and also conclude that Which organisation has more equitable distribution of compensations?

Expert Solution

1) organization 1

	X	Fi	Xi*Fi	Xi^2*Fi	(Xi-Xbar)^2*Fi
	5	655	3275	16375	573615.4776
	10	872	8720	87200	527401.5444
	15	1033	15495	232425	396556.0446
	20	1144	22880	457600	243623.0517
	25	1189	29725	743125	109419.7191
	30	1204	36120	1083600	25399.75409
	35	1212	42420	1484700	200.7137226
	40	1217	48680	1947200	35579.07957
	45	1220	54900	2470500	132131.531
	50	1222	61100	3055000	290071.0252
	55	1224	67320	3702600	509726.7973
	60	1225	73500	4410000	790753.3343

sum		13417	464135	19690325	3634478.073

mean = sum(Xi*Fi)/sum(Fi)
464135/13417= 34.5931

var= sum{(Xi-Xbar)^2*Fi}/(n-1)
3634478.0726/(13417-1) = 270.9062368

sd= sqrt(var)
16.46

CV = sd/mean*100%
16.4592/34.5931*100%
0.4758

2) organization 2

	X	Fi	Xi*Fi	Xi^2*Fi	(Xi-Xbar)^2*Fi
	5	950	4750	23750	1232061.991
	10	1657	16570	165700	1593671.711
	15	2108	31620	474300	1426389.496
	20	2488	49760	995200	1098525.045
	25	2645	66125	1653125	678186.8839
	30	2769	83070	2492100	335817.0064
	35	2825	98875	3460625	102127.5885
	40	2858	114320	4572800	2930.475336
	45	2870	129150	5811750	45631.15964
	50	2877	143850	7192500	232384.9532
	55	2882	158510	8718050	563855.6879
	60	2885	173100	10386000	1040104.12
	65	2888	187720	12201800	1661741.796
	70	2890	202300	14161000	2428378.447

sum		35592	1459720	72308700	12441806.36

mean = sum(Xi*Fi)/sum(Fi)
1459720/35592= 41.0126

var= sum{(Xi-Xbar)^2*Fi}/(n-1)
12441806.361/(35592-1) = 349.577319

sd= sqrt(var)
18.70

CV = sd/mean*100%
18.697/41.0126*100%
0.4559

mean of organization 2 is more reliable as it has less value of Coefficient of variation. hence Organization 2 more equitable distribution of compensations

orchestra answered 2 years ago

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