Coefficient of Variation

Coefficient of Variation

Ph-USA Guru

Today, we will

• Review the previous measures of variability.

• Define coefficient of variation.

• Solve for the coefficient of variations.

Please take down NOTES...

Copy important facts and formulas.

Poll

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Find the range: 4, 6, 3, 7, 9, 4, 2, 1, 4, 2

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Find the median: 4, 6, 3, 7, 9, 4, 2, 1, 4, 2

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What is the interquartile range (IQR) of the following data 4, 6, 3, 7, 9, 4, 2, 1, 4, 2?

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Given 4, 6, 3, 7, 9, 4, 2, 1, 4, 2, what is the mean?

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Use the value of the mean 4 to find the Mean Absolute Deviation: 4, 6, 3, 7, 9, 4, 2, 1, 4, 2.

Multiple Choice

Solve for the population variance: 4, 6, 3, 7, 9, 4, 2, 1, 4, 2.

• 4.5

• 5.6

• 4.1

• 6.5

Multiple Choice

Solve for the sample variance: 4, 6, 3, 7, 9, 4, 2, 1, 4, 2.

• 4.5

• 5.6

• 4.1

• 6.22

Multiple Choice

Given the following data 4, 6, 3, 7, 9, 4, 2, 1, 4, 2, what is the population standard deviation?

• 2.34

• 2.37

• 2.47

• 2.49

Multiple Choice

Given the following data 4, 6, 3, 7, 9, 4, 2, 1, 4, 2, what is the sample standard deviation?

• 2.34

• 2.37

• 2.47

• 2.49

Poll

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Overview:

The variance and the standard deviation are useful as measures of variation of the values of a single variable for a single population (or sample).

Overview:

 If we want to compare the variation of two variables we cannot use the variance or the standard deviation because:

1.   The variables might have different units.

2.   The variables might have different means.

Overview:

We need a measure of the relative variation  that will not depend on either the units or on how large the values are. This measure is the coefficient of variation (C.V.) which is defined by:

 $Coefficient\ of\ Variation\ =\ \frac{S\tan dard\ Deviation}{Mean}x\ 100\%$  

What is Coefficient of Variation?

Coefficient of Variation refers to the statistical measure which helps in measuring the dispersion of the various data points in the data series around mean and is calculated by dividing the standard deviation by mean and multiplying the resultant with 100.

Given the following data 4, 6, 3, 7, 9, 4, 2, 1, 4, 2, what is the coefficient of variation?

Step 1: Find the mean.

Given the following data 4, 6, 3, 7, 9, 4, 2, 1, 4, 2, what is the coefficient of variation?

Step 2. Subtract the mean from each score.

Given the following data 4, 6, 3, 7, 9, 4, 2, 1, 4, 2, what is the coefficient of variation?

Step 3: Take the square of the difference.

Given the following data 4, 6, 3, 7, 9, 4, 2, 1, 4, 2, what is the coefficient of variation?

Step 4: Compute for the standard deviation.

Given the following data 4, 6, 3, 7, 9, 4, 2, 1, 4, 2, what is the coefficient of variation?

 $cv\ =\frac{SD}{\overline{X}}\ x\ 100\%$  

Step 4: Use the formula.

Multiple Choice

Given the following data: 4, 6, 3, 7, 9, 4, 2, 1, 4, 2, find the population coefficient of variation.

 $cv_p=\frac{SD}{\overline{X}}\ x\ 100\%\ \ \ \ \ \ \ \ \$  

• 59.25%

• 62.25%

• 69.25%

• 72.25%

Multiple Choice

Given the following data: 4, 6, 3, 7, 9, 4, 2, 1, 4, 2, find the sample coefficient of variation.

 $cv_s\ =\ \frac{SD}{\overline{X}}\ x\ 100\%\ \ \ \$  

• 59.25%

• 62.25%

• 69.25%

• 72.25%

Poll

Do you have any question?

Open Ended

For those who says yes, please type it here.

Open Ended

Journal: When do we use coefficient of variation?