Question

Sample grade point averages for ten male students and ten female students are listed. Find the coefficient of variation for each of the two data sets. Then compare the results. Males 2.6 3.8 3.9 3.8 2.7 2.6 3.4 3.5 3.8 1.8 Females 2.7 3.9 2.2 3.8 3.5 4.1 2.1 3.8 3.9 2.5 The coefficient of variation for males is nothing​%. ​(Round to one decimal place as​ needed.)

Answer 1

No.of Sample	10
Mean	3.19
Standard Deviation	0.7171
Coefficient of Variance	0.2247
Step by Step Calculation: Input: 2.6, 3.8, 3.9, 3.8, 2.7, 2.6, 3.4, 3.5, 3.8, 1.8 Mean(µ) = (2.6 + 3.8 + 3.9 + 3.8 + 2.7 + 2.6 + 3.4 + 3.5 + 3.8 + 1.8)/10 Mean = 31.9/10 µ = 3.19

Standard deviation = sqrt [ sum ( Xi - mean )² / n - 1] =0.7171

= Sqrt( (1/10-1) * (2.6-3.19)2+(3.8-3.19)2+(3.9-3.19)2+(3.8-3.19)2+(2.7-3.19)2+(2.6-3.19)2+(3.4-3.19)2+(3.5-3.19)2+(3.8-3.19)2+(1.8-3.19)2)
= Sqrt( (1/9) * (-0.592 + 0.612 + 0.712 + 0.612 + -0.492 + -0.592 + 0.212 + 0.312+ 0.612 + -1.392))
= Sqrt( (1/9) * (0.3481 + 0.3721 + 0.5041 + 0.3721 + 0.2401 + 0.3481 + 0.0441 + 0.0961 + 0.3721 + 1.9321))
= Sqrt(0.51423241)
S= 0.7171
Coefficient of Variance = s/µ
= 0.7171 / 3.19
Coefficient of Variance = 0.2247

Male coefficient of variation = 0.2247 ~ 22.5 %

No.of Samples	10
Mean	3.25
Standard Deviation	0.7835
Coefficient of Variance	0.241
Step by Step Calculation: Input: 2.7, 3.9, 2.2, 3.8, 3.5, 4.1, 2.1, 3.8, 3.9, 2.5 Mean(µ) = (2.7 + 3.9 + 2.2 + 3.8 + 3.5 + 4.1 + 2.1 + 3.8 + 3.9 + 2.5)/10 Mean = 32.5/10 µ = 3.25

Standard deviation =

= Sqrt( (1/10-1) * (2.7-3.25)2+(3.9-3.25)2+(2.2-3.25)2+(3.8-3.25)2+(3.5-3.25)2+(4.1-3.25)2+(2.1-3.25)2+(3.8-3.25)2+(3.9-3.25)2+(2.5-3.25)2)
= Sqrt( (1/9) * (-0.552 + 0.652 + -1.052 + 0.552 + 0.252 + 0.852 + -1.152 + 0.552 + 0.652 + -0.752))
= Sqrt( (1/9) * (0.3025 + 0.4225 + 1.1025 + 0.3025 + 0.0625 + 0.7225 + 1.3225 + 0.3025 + 0.4225 + 0.5625))
= Sqrt( 0.61387225)
S= 0.7835

Coefficient of Variance = s/µ
= 0.7835 / 3.25
Coefficient of Variance = 0.241

Female coefficient of variation = 0.241 ~ 24.1 %

Female C.V. is greater than male C.V