Crop productivity is the main factor that determines the volume of crop production. When analyzing productivity, it is necessary to study the dynamics of growth for each crop or group of crops over a long period of time and identify reserves and opportunities for its further growth.

The yield level is the result of the influence of three complex factors - agrotechnical, natural and organizational. It fluctuates from year to year. To identify its development trend, you can use the moving average method during analysis. In this case, 5-10-year data on the productivity of a particular crop (or group of crops) is processed as follows: for the first 3-5 years, a simple average is calculated, then the date is shifted by 1 year and the average is determined again, etc. The resulting series usually shows an upward or downward trend in yield levels.

For example, in the analyzed farm over the past 7 years the following change in the level of grain crop yields has been observed:

1996 1997 1998 1999 2000 2001 2002

21,5 22,8 16,5 20,3 19,7 23,4 21,0

Until 1998, grain yields increased, and since 1998 they began to decline. However, such a conclusion is not entirely correct. Let us process this series using the moving average method.

Let's take the yield levels of the first three years and calculate the simple average, it will be equal to 20.3 c = (21.5 + 22.8 + 16.5) : 3. Then we will shift the date by one and again for three years (1997,1998, 1999) let's calculate the average, which will be equal to 19.8 c, etc.

As a result, we obtain a new dynamic yield series:

_____________________________________________________________

1996-1998 1997-1999 1998-2000 1999- 2001 2000 -2002

______________________________________________________________

20,3 19,8 18,8 21,1 21,4

______________________________________________________________

Thus, during the period from 1996 to 2002, the yield of grain crops on this farm tended to increase; it increased by 1.1 c (21.4 - 20.3).

Productivity is a quantitative, complex indicator that depends on many factors. Natural climatic conditions have a great influence on its level: 1) air temperature, 2) groundwater level, 3) amount of precipitation, 4) quality and composition of the soil, 5) terrain, etc. Therefore, when studying the dynamics of yield, it is necessary to take into account agrometeorological features of each year during the growing season and harvest.

All agrotechnical measures for growing crops, as well as high-quality execution of all field work in a short time and other economic factors have a great influence on productivity. In the process of analysis, it is necessary to study the implementation of the plan for all agrotechnical measures, determine the effectiveness of each of them, and then calculate the impact of each activity on the level of yield and gross production. To do this, underfulfillment or overfulfillment of the plan for the volume of each activity is multiplied by the planned level of its payback, and the change in payback is multiplied by the actual volume of the corresponding activity.

Thus, to determine the payback of fertilizers, three analysis methods can be used: experimental, calculated, correlation

The most accurate method is experimental. Its essence lies in the organization of field experiments. By comparing the yield of experimental plots where fertilizers were applied and control plots where they were not applied, it is possible to determine the increase in yield due to the applied fertilizers. However, this method is used only in experimental farms.

The majority of farms use a calculation method to determine the payback of fertilizers. According to this method, the calculation of additionally obtained products per 1 c of fertilizers is carried out in the following way: first, the yield from the natural fertility of the soil is calculated, for which the quality of the land in points is multiplied by the price of the point, which is determined by the regional agrochemical laboratory. Then the difference between the actual and estimated yield is divided by the number of applied fertilizers per 1 hectare of crops of a given crop and, thus, determine the increase in yield per 1 quintal of fertilizers (NPK)

Ok = (Uf – Ur): Kf, where

Ok – payback for 1 quintal of fertilizers,

Uf and Ur - actual and calculated yield levels;

Kf – the actual amount of fertilizer applied per 1 hectare of crop crops, centners

Calculation of payback of fertilizers

______________________________________________________________

Indicators Rye

______________________________________________________________

1. Soil quality, score 46

2.Price 1 point, c 0.36

3.Calculated yield level (from natural (46 × 0.36)

fertility c\ha 16.6

4. Actual yield, c\ha 25

5. Increase in productivity due to the application of fertilizers, c 8.4 (25-16.6)

6. Amount of applied fertilizers per 1 hectare, c 2

7. Actual payback of 1 c of fertilizer, c 4.2 (25-16.6): 2

8. Standard (planned) payback of 1 c of fertilizer, c 5.0

______________________________________________________________

These tables indicate that the payback plan for fertilizers when growing rye has not been fulfilled. A decrease in the payback of fertilizers can occur due to their imbalance, low quality, timing and methods of their application. Therefore, during the analysis process, all these reasons must be analyzed.

If there is a sufficient number of observations about the crop yield and the amount of fertilizer applied to it, correlation analysis can be used to determine the payback of fertilizers.

The increase in yield largely depends on the seeding rate, quality and variety of seeds. Reducing the seeding rate and the use of substandard seeds reduces crop yields. Therefore, during the analysis process, it is necessary to calculate how much the yield has decreased due to this factor. For example, if the norm is 450 plants per 1 sq. m actually sprouted 300, then we should expect that the yield of this crop will be lower than calculated by 20-30%.

In the process of analysis, they also find out which varieties are cultivated on the farm, and how timely variety change and variety renewal are carried out.

The yield of agricultural crops depends significantly on the applied crop rotations, which must be observed in each farm. In the introduction of crop rotations, there are two types:

1 - introduction, when the crop rotation project is transferred to nature, i.e. the fields are cut according to it;

2 - development, when the transition period is over, and agricultural crops are placed in the fields in accordance with the adopted scheme and crop rotation plan.

The structure of sown areas has a great influence on the average level of yield. For example, if among grain crops high-yielding crops have the largest share compared to the base year, then the average yield becomes higher.

To determine the effect of structure on the average yield level, you can use the index method using the following formula:

Device = ∑ У1 × S1 ∑ У1 × So

_________ : ___________

where: Y1 – yield of the reporting year, c\ha

S1 – area of ​​the reporting year, ha

So – base year area.ha

The timing of sowing and harvesting has a great influence on yield. The optimal time for sowing early grain crops is no more than 4-5 days, harvesting is 10-12 days. Deviation causes a decrease in yield.

The yield of agricultural crops, in addition to the listed factors, depends on a number of other agrotechnical measures: the quality and methods of soil cultivation, placement of crops in crop rotation fields, methods and timing of crop care, etc.

Crop types based on the state of the crops are determined by visually assessing the crops at different periods of their development. When assessing by eye, depending on the time of assessment, the density of seedlings, the degree of plant development, the degree of tillering, the corresponding density of plant standing, the size of the ear, etc. are taken into account. The assessment of crops is carried out by agronomic personnel and is expressed in a comparative qualitative characteristic (poor, below average, average, above average, good), points (1, 2, 3, 4, 5), centners, as a percentage of the average level.

Standing yield before timely harvesting can be determined in three ways:

• - eye-wise, by carefully inspecting the crops before harvesting (the so-called subjective method);
• - instrumentally, by selectively placing meters on crops before harvesting (objective method);
• - by calculating(by balance calculation method ) based on complete actual collection data and sample loss data.

The standing harvest before the start of timely harvesting and the barn harvest differ by the amount of actual losses. Therefore, knowing two of these three indicators, you can calculate the value of the third. However, standing yield and losses can only be estimated approximately. Therefore, balance equations between the noted indicators will have some kind of error in determining losses or standing crops.

Currently, statistics take the actual harvest as the main indicator. Until 1961, the amount of losses was determined selectively.

Both when assessing the standing crop yield and when analyzing the level of actual harvest per 1 hectare, it is necessary to clearly represent the constituent elements that directly determine the yield value. For example, the yield level of sugar beets depends on the number of plants (standing density) per hectare and the average weight of the roots, potatoes - on the number of bushes and the average weight of tubers per bush. For root and tuber crops, the value of these elements is often taken into account selectively when determining crop types. By comparing such values ​​with the corresponding standards for various stages of the growing season, a conclusion is drawn about the possible level of yield.

The yield level of cereal grain crops is composed of the following elements: the number of ears, the number of grains in an ear, the absolute weight of the grain. Therefore, having certain selective data on the value of these elements, grain yield per hectare in centners can be determined by the following formula:

U NK = K*Z*A 100000

Where TO-number of ears per 1 m2;

Z- number of grains in an ear;

A--absolute grain weight, i.e. weight of 1000 grains, g.

When assessing the yield on a farm by eye, areas with visible differences in yield are considered separately. After determining the yield for each field, the weighted average for the farm is found.

Species yield and productivity-- These are the sizes of the emerging crop and the emerging yield, established by the state of crops at certain points during the growing season, sometimes taking into account meteorological conditions and some manifestations of economic life.

For a long time, the assessment of crop yields has been included in the program of a special statistical report.

Harvest and standing yield represent the sizes of grown agricultural products, established before the start of timely harvesting. This category of harvest and yield of agricultural crops is determined either on the basis of a subjective generalized assessment for a certain date, or the results of selective imposition of meters on crops before harvesting or other materials. Yield and standing yield were also determined using a number of methods. So, for example, from 1947 to 1953, the determination of yield was carried out by the State Inspectorate for Determining Yields based on reports from collective and state farms on yields, the results of selective marking of crops before harvesting, data on yields at variety testing sites of the State Commission for Variety Testing Sites, meteorological materials stations, as well as information on the condition of crops throughout the growing season.

During this period, harvest and standing yield were considered the main assessment indicators of the level of development of crop production industries. Moreover, according to harvest and standing yield data, the amount of payment in kind for work performed by machine and tractor stations on collective farms was determined.

In subsequent years, the crop and standing yield were used for different purposes. On many farms, the size of the grown yield of a number of agricultural crops is determined during control threshing. Materials about this serve as a guide in harvesting work. State statistics bodies used data on control harvests among other materials in the study of losses during harvesting.

Under normal economic conditions harvest And normal economic productivity understand: harvest and standing yield minus the so-called normal losses at a given level of development of agricultural technology and production organization. From 1933 to 1939, these categories were considered basic in statistics. Gross harvest in the modern sense is the amount of collected and capitalized products from the harvested main, repeated and inter-row crops of certain agricultural crops. Since 1994, gross grain production in statistics has been taken into account as a final indicator in physical mass after processing (cleaning and drying). For ongoing monitoring of harvesting, gross harvest; is shown in the initially capitalized mass.

For vegetables in protected soil, the gross harvest is determined as the sum of products collected from all turnovers by type of structure. A general collection of vegetables from all types of protected ground structures is also established, as well as a general collection of vegetables from open and protected ground. The gross harvest of fruits, berries and grapes includes products collected not only from plantings at fruit-bearing age, but also from young plantings that have not been put into operation.

Average yield agricultural crops (harvest per 1 hectare) is determined by dividing the gross harvest from the main crops (without intermediate, repeated and inter-row crops) by the specified spring productive sown area of ​​these crops.

The fact that the spring productive area is used in the calculation stimulates the harvesting of the sown area. When calculating the average yield for the actually harvested area, it may turn out that a farm that allowed crops to die in summer, as well as left crops unharvested, will have a higher yield level compared to farms that completely harvested the entire sown area. For greenhouse vegetables, the average yield is found by dividing the gross harvest from all rotations by the used sown area for the first rotation. For perennial plantings, when calculating the average yield, the gross harvest from plantings at fruit-bearing age and the area of ​​only fruit-bearing plantings are taken into account, regardless of whether there was a harvest from these plantings in the reporting year or not.

Categories barn harvest And barn yield in statistics are interpreted ambiguously. It is believed that a barn harvest is a harvest that arrived in barns, warehouses and was recorded in one order or another. Or is it a harvest collected in the farm’s barns and documented. There is also an understanding of the barn harvest as the volume of harvest received by the farm. From 1954 to 1964, state statistics bodies published harvest data under the heading Gross harvest (barn harvest) of grain crops. In subsequent years, publications use only the term gross collection.

Harvest and yield are both forecast indicators.

Determination of TLD based on qualitative assessment of soil

The determination method was proposed by the Belarusian Research Institute of Soil Science and Agrochemistry:

TLD = Bp*Cb*K (13)

Bp – soil quality, point;

Cb – price of arable land point, kg;

K – correction factor to the point price for the agrochemical properties of the soil.

TLD =32*50*0.94=15c/ha

Determination of programmable yield (PrU).

The value of the programmed yield is determined taking into account the difference between the COU and the TLD, which is compensated by introducing calculated doses of mineral and organic fertilizers. Thus, the programmed yield is calculated as a TLD with the increase in yield that should be obtained through fertilizers.

PrU – programmable yield, c/ha;

Дnpk – dose of mineral fertilizers, kg/ha;

Оnpk – payback of 1t of organic fertilizers, kg/t of product;

100 – conversion factor from kg to c.

The PrU level can also be determined by knowing the relative increase from fertilizers:

(15)

Pood – increase in yield from fertilizers, %

Thus, the yield of spring barley of 32 c/ha will be a guideline for the development of a structural model of a highly productive plant and sowing in general, as well as crop cultivation technology.

Table 7. Calculation of fertilizer doses for the programmed harvest based on the removal of nutrients. The yield of spring barley is 32 c/ha

Lit. designation	Indicators	Unit measured
	Removal of nutrients from the soil by one centner of crop
	The total removal of nutrients necessary to obtain the programmed harvest (Bo=B*U)
	Soil nutrient uptake coefficient
	The amount of nutrients received by plants from the soil (Ip=P1*Kp*0.1)
	Added organic fertilizers
	Nutrients entered into the soil with manure (Np=10*Sm*O)
	Coefficient of nutrient absorption of organic fertilizers (per year of crop cultivation)
	Nutrients from organic fertilizers will be used by plants (Io=Np*K1-2*0.1)
	The total amount of nutrients that plants can receive from soil and organic fertilizers (I = In + Io)
	It is necessary to add nutrients with mineral fertilizers (D=Wo-Ip)
	Coefficient of nutrient absorption of mineral fertilizers
	Dose of mineral fertilizers that must be applied taking into account their utilization rate (Dm=D:Km*100)
	Contains nutrients in fats
	Application rate of mineral fertilizers (Mu=Dm:St)

As can be seen from the table, the calculation of doses of mineral fertilizers is carried out taking into account the content of nutrients in the soil, taking into account the elements that entered the soil with mineral fertilizers, as well as taking into account the coefficient of their absorption by plants. To obtain the programmed yield, according to the calculation data, it is necessary to add 44 kg/ha of nitrogen in the active substance, 33.5 kg/ha of active ingredient phosphorus, 33.5 kg/ha of active ingredient to the soil. potassium This will be equal to the application of: 2 c/ha of UAN, 2.4 c/ha of simple superphosphate and 1 c/ha of potassium chloride.

Harvest (gross harvest)- this is the total volume of production in physical terms obtained from the entire area of ​​harvested main, repeated and inter-row crops. The yield, measured in simple absolute units of mass (tons, kilograms, etc.), characterizes the overall scale of production for each individual type of crop product.

Accurate data on the size of the harvest (gross harvest) can be established only after harvesting. However, information about the harvest is necessary in earlier periods, for example, to determine the expected production of crop products, calculate the needs for equipment and vehicles before the start of harvesting work. For this purpose, yield indicators are used in relation to different periods (for example, phases) of plant development and periods of agricultural production.

The following yield indicators are distinguished: species yield, standing harvest before timely harvesting, actual harvest, net harvest.

Species harvest- this is the estimated expected yield, based on the state of the crops at different stages of plant development, which is usually determined by expert (eye) method, or by a selective method (by applying meters) taking into account the condition of the crops: density, development, appearance, etc. Definition and assessment species yield are common in economic practice and are aimed at making operational management decisions in the technology of crop production.

Standing harvest before harvesting - actually grown, but not yet harvested crop. Its size can be determined in the following ways:

· calculated - based on complete data on the actual harvest and selective data on losses during harvesting from typical areas;

· placing meters on crops before harvesting (if conditions permit);

· visual assessment of crops by experienced specialists.

Actual harvest(gross harvest) is the capitalized collection for each type of crop product after harvesting crops. The actual yield for a group of grains and leguminous crops can be expressed in the initially capitalized mass (bunker harvest) and in the mass after processing (barn harvest); for fiber flax and rapeseed - in bulk after processing, i.e. minus from the initial gross collection of unused waste and drying during harvest processing; For other types of crops, the harvest is determined by the physical mass of the actually received and capitalized gross harvest of products.

Clean Harvest- this is the actual harvest (usually after processing) minus the seeds of the corresponding types of agricultural crops spent on this harvest. The net yield can be calculated for grains, leguminous crops, flaxseeds, rapeseed, and potatoes.

Under productivity understand an indicator characterizing the average yield of each type of agricultural product per unit area. In agricultural organizations, it is practically customary to determine the yield per 1 hectare, in personal subsidiary plots - per are or 1 m2.

In connection with the differentiation of yield indicators (gross harvest), it is possible to calculate the corresponding yield indicators, i.e. species yield, standing yield before timely harvesting, actual yield, net yield.

In agricultural organizations of the Republic of Belarus, the yield of almost all agricultural crops (with some exceptions) is calculated per unit of spring productive area. The exception is annual and perennial grasses (for hay, green mass and seeds), for which the yield is determined per unit of actually harvested area.

In statistics, one should distinguish between individual (for one crop) and average (for a homogeneous group of crops) yield. To calculate the average yield, as a rule, the arithmetic weighted average method is used (2):

where is the average yield;

Individual yield of each crop;

The area under which this crop is sown.

The procedure for determining the average yield for the group of grains and leguminous crops in the Niva agricultural enterprise is given in table. 5.

As can be seen from the data given in table. 5., with crop yield fluctuations from 20 to 40 c/ha, the average yield for the group of grains and leguminous crops in the Niva agricultural enterprise was 31.9 c/ha.

Both individual and average crop yields are the most important indicators that characterize not only the level of use of agricultural land, but also largely determine the efficiency of agricultural enterprises, farms, peasants, and personal subsidiary plots.

Table 5. Calculation of the average yield of grain and leguminous crops in the Niva agricultural enterprise

Cultures	Sown area, ha	Productivity, c/ha	Gross harvest, t
Winter rye
Winter wheat
Spring wheat

As noted above (paragraphs 1, 2), in the Republic of Belarus, agricultural yields are formed in all categories of farms. The dynamics of these indicators are shown in table. 6..

Table 6. Harvest (gross yield) and yield of agricultural crops

Groups and types of crops	Harvest, thousand tons	Productivity, c/ha
Cereals and legumes
Including:
tertiary
pulses
Flax fiber
Sugar beet
Potato
Fodder root crops
Corn for green mass
Perennial grass hay

As the data in table shows. 6, in the Republic of Belarus in 2014. compared to 2010 There was a positive trend in yield and productivity of almost all agricultural crops. The harvest and productivity of grain crops (especially rye, wheat, barley, oats), flax fiber, rapeseed, potatoes, vegetable crops, and corn for green mass have increased significantly. Despite the decline in sugar beet yields, the gross yield of this crop has increased significantly due to the expansion of the sown area. The decrease in the yield of rye, fodder root crops, and perennial grass hay (with a simultaneous increase in yield) was due to a significant reduction in the acreage under these crops.

It is advisable to note that the yield of each agricultural crop, calculated per unit of sown area in physical terms, makes it possible to evaluate and compare the work of farms only for specific crops, provided that natural soil fertility is equal. Therefore, when objectively assessing the work of agricultural enterprises, along with traditional crop yields, it is logical to calculate the gross yield for each crop per 1 point-hectare of sown area. Let’s say that in one farm the yield of winter rye was 50 c/ha on arable land with a quality rating of 50 points, and in another - 30 c/ha, where the quality of the land was rated 30 points. Despite the seemingly better work of the first farm compared to the second, both farms worked equally, since winter rye per point-hectare in both farms accounts for one hundredweight of grain.

2.1 Grouping of farms by grain yield levels

The most important method of statistics is the grouping method. Grouping and summarizing the material involves dividing the entire mass of units into homogeneous groups and subgroups, calculating the results for each group and subgroup, and formatting the results obtained in the form of a statistical table. Groupings make it possible to identify units of different quality from all cases and to show features that develop in different conditions.

Tasks facing the group:

1. Identification of those parts of a mass phenomenon that are homogeneous in quality and conditions of development, and in which the same natural influences of factors operate;

2. Study and characterization of the structure and structural changes in the populations under study;

3. The influence of the relationship between individual characteristics of the phenomenon being studied.

The main issue of the grouping method is the choice of a grouping characteristic, the correct choice of which determines the results of the grouping and the work as a whole.

After selecting a grouping characteristic, it is important to divide the population units into groups.

The selected groups must be qualitatively homogeneous, and also have a sufficiently large number of units, which will allow them to display typical features characteristic of mass phenomena. Therefore, much attention is paid to determining the number of groups and their boundaries. To resolve this issue, the type of grouping, the nature of the grouping characteristic and the objectives of the study are taken into account.

The initial data for analyzing the yield of grain crops is presented in “Appendix A”.

Let us construct a ranked series of distribution of farms in the region, in which all units of the population are arranged according to increasing grouping characteristics, i.e. on the yield of grain crops.

Table 2.1.1 Ranking of farms by grain yield

Farm No.	Farm name	Productivity of grain crops, c/ha	Old farm number
	SEC Agidel
	LLC Voskhod
	SEC Nadezhda
	SPK AF Kama
	JSC Tugan Yak
	SPK AF Mayak
	SPK AF Kolos
	LLC Batyr
	SPK AF Mir
	SEC Razdolye
	Khan Murza LLC
	LLC NPO Bashkirskoe
	LLC PH Kushnarenkovskoe
	Phloema-Agro LLC
	Kupay LLC

Let's depict the ranked series graphically in the form of Galton's Ogiva graph. (Fig. 2.1.1)

Figure 2.1.1 Ranked series by grain crop yield, c/ha.

By assessing the intensity of change in the value of a grouping characteristic from one unit of the population to another, we can distinguish groups.

After analyzing graph 2.1.1, you can divide the population into 3 groups with equal intervals, the value of the equal interval is determined by the following formula:

Xmax is the maximum value of the attribute in the studied ranked series,

Xmin is the minimum value of the attribute in the studied ranked series,

n - number of groups (n=3).

i=(17.11-1.73) / 3

And so the interval is 5.13

Now let's construct an interval series of distribution of farms.

Table 2.1.2 Interval series of distribution of farms according to the yield of grain crops, centners per 1 ha

For clarity, we build a graph of the interval variation series of farm distribution - a histogram.

Figure 2.1.2 Interval series of distribution of farms by grain yield.

The diagram shows that most farms belong to the first group with a yield range of 1.73-6.85, farms belong to group II with a range of 6.85-11.98 thousand rubles, and group III includes farms with yield of which more than 11.98 c per 1 hectare.

To carry out the next stage of analytical grouping, as well as to calculate such indicators as the average grain yield, c/ha and the average cost of 1 c of grain, rub. for 3 groups we will use Table 2.1.3 and Table 2.1.4.

Table 2.1.3 Simple analytical grouping worksheet

Groups of farms by grain yield, centners per hectare	Name of farms	Cultivated area of ​​grains, hectares.	Gross grain harvest, centners	Total cost, thousand rubles.
	SEC "Agidel"
	LLC "Voskhod"
	SEC "Nadezhda"
	SEC "AF Kama"
	JSC Tugan Yak
	SPK "AF Mayak"
	SPK "AF Kolos"
	LLC "Batyr"
	SPK "AF Mir"
	SEC "Razdolye"
Total for group I
	Khan Murza LLC
	LLC NPO Bashkirskoe
Total for group II
III group	LLC PH Kushnarenkovskoe
	Phloema-Agro LLC
	Kupay LLC
Total for group III

Table 2.1.4 Summary table of simple analytical grouping

Group number	Groups of farms by grain yield, centners per hectare	Number of farms	Average grain yield, c/ha.	Average cost of 1 quintal of grain, rub

Thus, the group showed that the average grain yield increased from 4.35 to 16.50 c/ha, which averaged 5.51 c/ha for all groups. The average cost of 1 centner of grain in the first group was 683.34 rubles, and in the second group it was 269.55 units more; on average for the three farms this figure was 709.54 rubles.

Now let us study the nature of variation in the yield of grain crops. The difference in individual values ​​of a characteristic within the population being studied is called variation. To study variation, variation indices are calculated, with the help of which a conclusion is drawn about the reliability of the calculated average values.

Table 2.1.5 Initial variation data

Group of households according to the yield of grain crops per 1 ha	Number of farms	Average value of the interval

The study of variation (deviations of individual values ​​from the average) is of great importance.

Firstly, the variation indicators serve as a characteristic of the typicality of the average itself. The smaller the variation, the more representative the typical average.

Secondly, variation indicators serve to characterize the uniformity of the work of enterprises and their divisions.

Variation indicators:

Absolute variation indicators:

Variation range:

Average linear deviation:

Dispersion:

Standard deviation:

Relative variation indicators:

The coefficient of variation:

Oscillation coefficient:

Linear coefficient of variation:

Distribution form indicators:

Asymmetry:

Relative range of variation (VR) or coefficient of oscillation shows the fluctuation of extreme values ​​around the average.

Relative linear deviation (Vd) characterizes the proportion of absolute deviation values ​​from the average value. The coefficient of variation can be used to judge the homogeneity of the population being studied.

Table 2.1.6. Indicators of variation and forms of distribution by typical groups and for the economy as a whole

The coefficient of variation is > 33%, which means that the population being studied is heterogeneous, and the average value found is not quite reliable and does not express the typical level of the entire population being studied.

The standard deviation shows how much on average the actual value of a characteristic differs from its average value. In our case, the standard deviation for the entire farm is 0.92 c/ha.

If the asymmetry is greater than zero, then the asymmetry is right-sided, but if it is less, then it is left-sided. The greater the asymmetry index, the greater the degree of skewness of the distribution. From the table you can see that in the economy as a whole the asymmetry is right-sided.

If the kurtosis is greater than zero, then we get a peaked distribution; if it is less than zero, then we get a flat-topped distribution. In our case, the distribution across the economy as a whole is peaked.

2.2 Calculation of general indicators for typical groups

yield indicator index analysis

To analyze the differences between typical groups, we will calculate generalizing indicators (Appendix B).

By analyzing the data in this table by group, conclusions can be drawn. The indicators of the third group are at an average level, despite the fact that the number of farms is four times smaller compared to the first group. In terms of average yield, the third group takes first place. The second group also shows good results.

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