Question

Sample grade point averages for ten male students and ton female students are listed. Find the coofficient of variation for each of the two data sets. Then compare the results Males 26 35 3.8 3.9 27 25 Females 29 36 2.1 39 34 39 The coefficent of variation for males is 22.7% (Round to one decimal place as needed) The coefficent of variat on sor females is | |% (Round to one decimal place as needed) 36 33 1.9 3.9 39 38 18 25 ' Incorrect

Answer 1

1. for Males           

x	(x-x̅ )	(x - x̅)²
2.6	-0.56	0.3136
3.5	0.34	0.1156
3.8	0.64	0.4096
3.9	0.74	0.5476
2.7	-0.46	0.2116
2.5	-0.66	0.4356
3.6	0.44	0.1936
3.3	0.14	0.0196
3.9	0.74	0.5476
1.8	-1.36	1.8496
31.6		4.644

Mean (x̅) = ∑x/n   =3.16   =31.6/10   =3.16

Sample standard deviation = √(∑(x - x̅)²/n-1)                = √(4.644/9)     =0.718331

Coefficient of variation = Sample standard deviation/Mean     =0.718331/3.16 = 0.22732

= 0.22732*100     =22.73201

=22.7 %

2. Simillarly we calculate for Feamale

Mean (x̅) = ∑x/n   =31.9/10    =3.19

Sample standard deviation = √(∑(x - x̅)²/n-1)                = √(5.509/9)     = 0.782375

Coefficient of variation = Sample standard deviation/Mean     =0.782375/3.19   =0.245259

=0.245259*100         =24.52587      

=24.5%

Hence we observe that Coefficient of variation for Females is greater than for Males.