Advice 1: How to calculate the coefficient of variation

In the study of variation – differences of individual characteristic values in units of the investigated range – counting a number of absolute and relative indicators. In practice the greatest application among the relative indices found the coefficient of variation.
How to calculate the coefficient of variation
To find the coefficient of variation, use the following formula:
V=σ/Khsr, where
σ - standard deviation,
Khsr – the arithmetic mean of variational series.
Note that the coefficient of variation in practice is not only used for the comparative assessment of variations, but also to characterize the homogeneity of the population. If this figure is less than 0,333, or 33.3%, variation of the characteristic is considered weak, and if more 0,333 strong. In case of strong variations of the statistical population under review is considered to be heterogeneous, and the average value is atypical, so it cannot be used as a General indicator of the aggregate. The lower limit of the coefficient of variation is considered to be zero, there is no upper limit. However, with the increase in the variation of the characteristic increases and its value.
When calculating the coefficient of variation you have to use the standard deviation. It is defined as the square root of the variance, which in turn you can find as follows: D = Σ(X-Khsr)^2/N. in Other words the variance is the average squared deviation from the mean value. The standard deviation determines how much the average are rejected specific performance of the series from their mean value. It is an absolute measure of the oscillatory characteristic, and so clearly interpreted.
Consider the example of calculation of coefficient of variation. Consumption of raw materials per unit of output, produced by first technology is Khsr=10 kg, with an average standard deviation σ1=4, according to the second technology – Khsr=6 kg, with σ2= 3. When comparing the standard deviation it is possible to make a wrong conclusion that the variation of the consumption of raw materials at the first technology is more intense than the second. The coefficients of variation V1=0.4 or 40% and V2=0.5 or 50% make the opposite conclusion.

Advice 2: How to find the coefficient of variation

Mathematical statistics is impossible without studying variation and, in particular, the calculation of the coefficient of variation. He has received the greatest application in practice due to simple calculation and clarity of results.
How to find the coefficient of variation
You will need
  • - variation of several numeric values;
  • calculator.
First, find the sample mean. To do this, add up all the values of the variational series and divide them by the number of study items. For example, if you want to find the coefficient of variation of three indicators 85, 88 and 90 to calculate the sample mean we need to add these values and divide by 3: x(CP)=(85+88+90)/3=87,67.
Then, calculate the margin of error the sample mean (standard deviation). For this purpose from each sample subtract the average value found in first step. Lift all the difference in a square and fold the received results among themselves. You got the numerator of the fraction. In the example the calculation would look like this: (85-87,67)^2+(88-87,67)^2+(90-87,67)^2=(-2,67)^2+0,33^2+2,33^2=7,13+0,11+5,43=12,67.
To get the denominator, multiply the number of sample points n (n-1). In the example this would look like 3x(3-1)=3x2=6.
Divide the numerator by the denominator and from the resulting numbers to Express a fraction to get the margin of error SX. You get 12,67/6=2 and 11. The root of 2.11 is equal to 1.45.
Proceed to the main point: find the coefficient of variation. To do this, divide the margin of error for the sample mean found in the first step. In the example of 2.11/87,67=0,024. To get the result in percent, multiply the resulting number by 100% (0,024х100%=2,4%). You have found the coefficient of variationand is equal to 2,4%.
Please note, the estimated coefficient of variation is quite small, so the variation of the sign is considered weak and the target population can be considered homogeneous. If the ratio exceeded the 0.33 (33%), the average value cannot be considered typical, and study through it the totality of would be wrong.
Useful advice
You can check the result by eye, to ensure his fidelity. Rate about the sample elements, if they are almost identical, you should get a small percentage. The greater the scatter of the index, the greater the coefficient of variation.
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