Mathematical statistics is inconceivable without studying a variation and, including, calculation of coefficient of a variation. He received the biggest practical application thanks to simple calculation and presentation of result.
It is required to you
- - variation from several numerical values;
- - calculator.
Instruction
1. At first find selective average. For this purpose put all values of a variational series and divide them into the number of the studied units. For example, if it is required to find coefficient of a variation of three indicators 85, 88 and 90 for calculation of selective average it is necessary to add these values and to divide into 3: x (sr)= (85+88+90)/3=87.67.
2. Then calculate an error of representativeness of selective average (average quadratic deviation). For this purpose subtract the average value found in the first step from each value of sample. Square all differences and put the received results among themselves. You received fraction numerator. In an example the calculation will look so: (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.
3. To receive a denominator of fraction increase quantity of sample units of n by (n-1). In an example it will look as the 3rd (3-1)=3х2=6.
4. Divide numerator into a denominator and from the received number express fraction to receive an error of representativeness of Sx. At you 12.67/6=2.11 will turn out. The root from 2.11 is equal to 1.45.
5. Start the most important: find variation coefficient. For this purpose divide the received representativeness error into selective average, found in the first step. In an example 2.11/87.67=0.024. To receive result as a percentage, increase the received number by 100% (0.024Õ100%=2.4%). You found variation coefficient, and it is equal to 2.4%.
6. Pay attention, the received variation coefficient quite insignificant therefore the variation of sign is considered weak and the studied set it is quite possible to consider uniform. If the coefficient exceeded 0.33 (33%), then average size could not be considered typical, and it would be incorrect to study in it set.