Question

3.3 3.0 2.3 2.6 2.5 2.8 2.7 2.9 2.4 2.4 2.0 3.6 3.1 3.9 2.6 4.0 1.7 3.0 3.1 2.0 1.9 2.1 1.9 2.1 3.4 Calculate the coefficient of variation.

Answer 1

Mean(µ) = (3.3 + 3.0 + 2.3 + 2.6 + 2.5 + 2.8 + 2.7 + 2.9 + 2.4 + 2.4 + 2.0 + 3.6 + 3.1 + 3.9 + 2.6 + 4.0 + 1.7 + 3.0 + 3.1 + 2.0 + 1.9 + 2.1 + 1.9 + 2.1 + 3.4)/25
Mean = 67.3/25
µ = 2.6919

µ = 2.6919


= √( (1/25-1) * (3.3-2.6919)2+( 3.0-2.6919)2+( 2.3-2.6919)2+( 2.6-2.6919)2+( 2.5-2.6919)2+( 2.8-2.6919)2+( 2.7-2.6919)2+( 2.9-2.6919)2+( 2.4-2.6919)2+( 2.4-2.6919)2+( 2.0-2.6919)2+( 3.6-2.6919)2+( 3.1-2.6919)2+( 3.9-2.6919)2+( 2.6-2.6919)2+( 4.0-2.6919)2+( 1.7-2.6919)2+( 3.0-2.6919)2+( 3.1-2.6919)2+( 2.0-2.6919)2+( 1.9-2.6919)2+( 2.1-2.6919)2+( 1.9-2.6919)2+( 2.1-2.6919)2+( 3.4-2.6919)2)
= √( (1/24) * (0.60812 + 0.30812 + -0.39192+ -0.09192 + -0.19192 + 0.10812 + 0.00812+ 0.20812 + -0.29192 + -0.29192 + -0.69192+ 0.90812 + 0.40812 + 1.20812 + -0.09192 + 1.30812 + -0.99192 + 0.30812 + 0.40812 + -0.69192 + -0.79192 + -0.59192 + -0.79192 + -0.59192 + 0.70812))
= √( (1/24) * (0.36978561 + 0.09492561 + 0.15358561 + 0.00844561 + 0.03682561 + 0.01168561 + 6.561E-5 + 0.04330561 + 0.08520561 + 0.08520561 + 0.47872561 + 0.82464561 + 0.16654561 + 1.45950561 + 0.00844561 + 1.71112561 + 0.98386561 + 0.09492561 + 0.16654561 + 0.47872561 + 0.62710561 + 0.35034561 + 0.62710561 + 0.35034561 + 0.50140561))
= √ 0.40487769
σ= 0.6363

Coefficient of Variance = σ/µ
= 0.6363 / 2.6919
Coefficient of Variance = 0.2363