Cross-correlation analysis of the productivity of sugar beets and factors, that it is formed

      For a yield: 36,77<36,91<36,98

      Majority governed executed.

     As we marked higher, except for the averages of degree, descriptive descriptions of row of distributing of sign are used in statistics — Moda (Мо) and Mediana (Ме).

      Variants name in statistics the size of sign a fashion, which more frequent all meets in an aggregate. In the interval rows of distributing a fashion is determined after such formula: 

       ,

      where х₀ – minimum limit of modal interval, і – size of modal interval, f₁ – frequency of interval, that is preceded to modal , f₂ – frequency of modal interval, f₃ – frequency of interval which stands after modal.

      From data of tabl. 6,8,10 will define a fashion on effective and factor signs:

      Мо_(Х1)= 36,94 +1,54 = 37,81 c.f.un.;

      Мо_(Х3)= 92,8 +1,4 = 93,64 chairmen ;

      Мо_(Y)= 37,24 +1,98 = 37,9 c;

      Median - it variant which stands in the middle of grade row and divides him in half, that row, located in the order of growth or slump of variants.

      A median in the interval row of distributing is determined after a formula: 

                                      Ме= ,

      where х₀ – minimum limit of median interval; і- size of median interval; - semisum of frequencies (half of units of aggregate); S_Me-1- sum of story frequencies which stand before a median interval; f_Me – frequency of median interval.

      From data of tablet. 6,8,10 will define a median. Median will be a that interval, sum of story frequencies of which the first exceeds the half of aggregate: 

      Ме_(Х1)= =38,48(c.f.un.)

     Ме_(Х2)= =93,73(chairmen)

      Ме_(Y)= =37,39(c). 
 
 
 

     2.5 Variation of signs and indexes of their measuring 

     Averages give summarizing description of aggregates on some varying sign. Simply at the that mean value of the probed sign separate aggregates substantially differ between itself after composition and size of deviations from middle. The studies of size of rejections and their distributing utillize homogeneities of aggregate for an estimation, than more small feet of oscillation of sign, that one more native aggregate.

     Variation is a change of size of sign in a statistical aggregate. Variation is the result of action on unit of aggregate of natural, climatic, economic and other factors, and also individual features of separate units.

     The study of variation of sign enables to define, what factors and in which measure influence on the size of the probed signs.

     Study of variation of sign it is necessary for scientific organization of selective supervision, dispersion and cross-correlation analysis.

     For a study variation of sign utillize such indexes as:

• scope of variation (R),
• mean linear deviation (d),
• dispersion and standard deviation (δ², δ),
• coefficient of variation (V).

     A scope of variation is a difference between the most and the least value of sign:

     R = X_max –X_min.

     Mean linear deviation - middle arithmetic from the absolute values (modules) of rejections of separate values of variation sign from his mean value.

     Mean linear deviation is calculated after such formulas: for frill information: 

     

;

     for the grouped information, when frequencies are different: 

     

.

     Dispersion is an average from the squares of rejections variant from an average (δ² ), and root the square from dispersion is named standard deviation.

     : Dispersion is calculated after formulas

      for the not grouped information –

      

;                                        ;

     for the grouped information, when frequencies are different:

     

                                     

     All are considered the indexes of variation characterize the absolute size of rejection and expressed in those metages in which variants are shown and middle. For comparative description of variation of rows with different levels the relative index of variation - coefficient of variation is used.

     A coefficient of variation is attitude of standard deviation toward an average, shown in percents: 

     

.

     He evidently characterizes variation of sign and is to a certain extent reliability middle. If the coefficient of variation anymore 33 %, it means that middle not very much reliable for this aggregate and an aggregate on this sign is heterogeneous.

     Will expect the simple indexes of variation. 

Table 18. A weekend and calculation information is for the calculation of simple indexes of variation

 

     Scope of variation:

     For the expense of forages R = X_1max –X_1min=43.1 – 35.4=7.7(ц.к.од.);

     For the output of calves  R = X_2max –X_2min= 97 - 90=7(голів);

     For will milk R = Y_max –Y_min=41,2 -31,3=9,9(ц). 

     Mean linear deviation:

     For the expense of forages ;

     For the output of calves ;

     For will milk

     Dispersion:

     For the expense of forages ;

     For the output of calves ;

     For will milk .

     Standard deviation:

     For the expense of forages ;

     For the output of calves ;

     For will milk .

     Coefficient of variation:

     For the expense of forages  ;

     For the output of calves  ;

     For will milk  .

     Expecting the basic indexes of variation we can assert that all of three aggregates (after the charges of forages, output of calves and yield) is homogeneous, as a coefficient of variation in all three cases more small 33%.

     We can mark in addition, that the middle level of yield on a cow for aggregates makes 36,91 с at the same time he hesitates on ± 2,258с or on 6,2% in relation to a middle level, the middle level of the utillized forages makes 39,09с.f.un. and he in same queue hesitates on ±2,06c.f.un. or on the 5,3% in relation to a middle level, also at to the middle output of calves for aggregates in size of  93,7 chairmen it hesitates on ±2,08 marks or on 2,2% in relation to a middle level.

     Separately will expect the self-weighted indexes of variation. 
 

Table 19. Calculation of the self-weighted  indexes of variation for to the charges of forages

 

     As our information  is presented as an interval variation row of distributing, utillize formulas for the grouped information.

      Mean linear deviation - = ;

     Dispersion - = ;

     Standard deviation - = .

     Will confirm the calculation of dispersion, expecting it the method of counting out from the conditional beginning (by the method of moments). 

Table 20. Calculation of dispersion  for to the charges of forages by the method of counting out from a conditional zero

 
 

      Certain and got before will put information to the formula and will calculate the size of dispersion: 
 

      

      Size of dispersions, and consequently and standard deviation coincides. 
 
 

   Table 21. A calculation of the self-weighted  indexes of variation is on the output of calves

 
 

     As our information is presented as an interval variation row of distributing, utillize formulas for the grouped information.