Question

In: Math

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...

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.

Solutions

Expert Solution

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

milcah answered 1 year ago
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