Question

Google's stock (GOOG) was tracked for 10 days, showing closing prices of 1,130.07; 1,100.85; 1,123.42; 1,094.08; 1,102.64; 1,103.12; 1,103.96; 1,131.74; 1,137.98; 1,078.23. Calculate the coefficient of variation of the dataset.

Answer 1

Solution:
Coefficient of Variation can be calculated as
Coefficient of Variation for sample = (S/xbar)*100%
Xbar can be calculated as
Xbar =(Xi)/n = (1,130.07+ 1,100.85+ 1,123.42+ 1,094.08+ 1,102.64+ 1,103.12+ 1,103.96+ 1,131.74+ 1,137.98+ 1,078.23)/10 = 11106.09 /10 = 1110.609
Standard deviation can be calculated as
Standard deviation =sqrt((X-Xbar)^2/(n-1))

X	Xi-Xbar	(Xi-Xbar)^2
1130.07	19.461	378.730521
1100.85	-9.759	95.238081
1123.42	12.811	164.121721
1094.08	-16.529	273.207841
1102.64	-7.969	63.504961
1103.12	-7.489	56.085121
1103.96	-6.649	44.209201
1131.74	21.131	446.519161
1137.98	27.371	749.171641
1078.23	-32.379	1048.399641
	Sum(Xi-Xbar)^2	3319.18789

Standard deviation S = sqrt(3319.18789/9) = 19.20
So Coefficient of variation = (19.20/1110.609)*100% = 1.73%