Can the increase be more than 100? Average indicators in the dynamics series

Let's find the growth rate of indicators, the growth rate of indicators. Based on the basic indicators, we will calculate the indicators of intensification of production resources contained in formula (1).

We will find the growth rate by relating the data from the second year to the first year and multiplying by 100%. We find the growth rate by subtracting 100% from the resulting figure.

1. The growth rate of products sold is equal to:

(3502: 2604) x 100% = 134.5%,

The growth rate is:

134,5% - 100% = 34,5%;

2. The personnel growth rate is:

(100: 99) x 100% = 101.0%,

The growth rate is:

101,0% - 100% = 1,0%;

3. The growth rate of wages is equal to:

(1555: 1365) x 100% = 113.9%,

The growth rate is:

113,9% - 100% = 13,9%;

4. The growth rate of material costs is equal to:

(1016: 905) x 100% = 112.3%,

The growth rate is:

112,3% - 100% = 12,3%;

5. The growth rate of depreciation is equal to:

(178:90) x 100% = 197.8%,

The growth rate is:

197,8% - 100% = 97,8%;

6. The growth rate of non-current assets is equal to:

(1612: 1237) x 100% = 130.3%,

The growth rate is:

130,3% - 100% = 30,3%;

7. The growth rate of current assets is equal to:

(943: 800) x 100% = 117.9%,

The growth rate is:

117,9% - 100% = 17,9%;

We will enter the calculation results in Table 7.

For base year:

1. Payability of products: 1365: 2604 = 0.524194;

2. Material consumption of products: 905: 2604 = 0.524194;

3. Depreciation capacity of products: 90: 2604 = 0.034562;

4. Capital intensity of production: 1237: 2604 = 0.524194;

800: 2604 = 0,307220.

For the reporting year:

1. Product payment intensity: 1555: 3502 = 0.444032;

2. Material consumption of products: 1016: 3502 = 0.290120;

3. Depreciation capacity of products: 178: 3502 = 0.050828;

4. Capital intensity of production: 1612: 3502 = 0.460308;

5. Ratio of fixation of current assets:

943: 3502 = 0,269275.

We will enter the results into Table 8.

Table 8.

Intensification indicators

production resources

We will calculate the methodology for analyzing the five-factor model of return on assets using the method of chain substitutions and consider the impact on the profitability of the five above-mentioned factors.

First, let's find the profitability value for the base and reporting years:

for base year

Krentv(0) = 1-(0.524194+0.347542+0.034562) = 1-0.906298 = 0.1198, i.e. 11.98%

0,475038+0,307220 0,782258

for the reporting year

Krentv(1) = 1-(0.444032+0.290120+0.050828) = 1-0.78498 = 0.2947, i.e. 29.47%

0,460308+0,269275 0,729583

The difference in the profitability ratios of the reporting and base years was 0.1749, or as a percentage - 17.49%.

Now let's look at how the five factors mentioned above contributed to this increase in profitability.

1. Influence of labor intensity factor

Krentv|U = 1-(0.444032+0.347542+0.034562) = 1-0826136 = 0.2223, i.e. 22.23%

0,475038+0,307220 0,782258

0.2223 - 0.1198 = 0.1025, i.e. 10.25%

2. Influence of material consumption factor.

Krentv|M = 1-(0.444032+0.290120+0.034562) = 1-0.768714 = 0.2957, i.e. 29.57%

0,475038+0,307220 0,782258

0.2957 – 0.2223 = 0.0734, i.e. 7.34%

3. The influence of the depreciation capacity factor.

Krentv|A = 1-(0.444032+0.290120+0.050828) = 1-0.78498 = 0.2749, i.e. 27.49%

0,475038+0,307220 0,782258

0.2749 – 0.2957 = -0.0208, i.e. -2.08%

4. The influence of the capital intensity factor.

Krentv|F = 1-(0.444032+0.290120+0.050828) = 1-0.78498 = 0.2801, i.e. 28.01%

0,460308+0,307220 0,767528

0.2801 – 0.2749 = 0.0052, i.e. 0.52%

5. The influence of the working capital turnover factor.

In order to calculate the influence of the working capital turnover factor, instead of the base turnover, we substitute the reporting figure. Let's get the reported profitability. Comparing reported profitability with previous conditional profitability will show the impact of turnover:

0.2947 – 0.2801 = 0.0146, i.e. 1.46%.

In conclusion, let’s make a summary of the influence of factors on the deviation of profitability of the 2nd year compared to the 1st year:

3.2. Comprehensive assessment of the efficiency of economic activities

based on extensiveness and intensity

Let us consider the calculations of the proposed comprehensive assessment methodology using the example of Finzhilservice LLC data for 2 years: 1st year – base year, 2nd year – reporting year. The initial data is presented in Table 7 “Basic indicators for the enterprise for two years.”

We will enter the results of the analysis into Table 9.

Table 9.

Summary analysis of intensification and efficiency indicators

Our engine for creating online calculators has new functionality - the ability to enter an arbitrary number of values ​​for calculations, in other words, an input table has appeared. The user adds/edits/deletes values, and the calculator calculates them.

Taking advantage of this, I immediately created a calculator for calculating analytical indicators of statistical time series.
Moreover, a user with the nickname Svetlana has long been asking for a calculator that calculates the average growth rate. Finally it became possible. But first things first.

Let's start with the theory.

Rows of speakers are called series of indicators arranged in chronological order that characterize the change in any value over time. Dynamics series include two main elements: time indicators - t and corresponding magnitude indicators - Y.

The dynamics series are divided into momentary And interval.
Moment dynamics series display the state of the studied quantity at a certain point in time. Interval series display the state of the studied quantity for individual time intervals.

Let me give you an example. Let's say that on January 1, bread costs 13 rubles, on February 1 - 14 rubles, on March 1 - 15 rubles, this is a moment series. If we bought 10 loaves of bread in January, 12 loaves in February, 14 loaves in March, this is an interval series. Note that the interval series has the property of summation, i.e. the indicators can be added up and you get something meaningful, for example, bread consumption for three months.

With the chain method, each subsequent indicator is compared with the previous one, with the basic method - with the same indicator taken as the basis of comparison. This is usually the first indicator in a series.

Let's look at some analytical derivative indicators:

Analytical Derivatives

1. Absolute increase
The difference between the values ​​of two indicators of a dynamics series.

Basic absolute growth - the difference between the current value and the value taken as a constant comparison base

Chain absolute increase - the difference between the current and previous values

2. Growth rate
The ratio of two levels of a series (can be expressed as a percentage).

Basic growth rate - the ratio of the current value and the value taken as a constant basis of comparison

Chain growth rate - the ratio of the current and previous values

3. Rate of increase
The ratio of absolute growth to the compared indicator.

Basic growth rate - the ratio of the absolute basic growth and the value taken as a constant basis of comparison

Chain growth rate - the ratio of absolute chain growth and the previous value of the indicator

4. Acceleration

Absolute acceleration is the difference between the absolute growth for a given period and the absolute growth for the previous period of equal duration. Can only be measured in chain mode

Relative acceleration - the ratio of the chain growth rate for a given period and the chain growth rate for the previous period

5. Rate of buildup
The ratio of chain absolute increases to the level taken as a constant base of comparison

6. Absolute value of one percent increase
The ratio of absolute growth to growth rate, expressed as a percentage.
After expansion, the formula simplifies to

To obtain general characteristics of the dynamics of the series under study, we calculate average dynamics.

Average dynamics

1. Average level
Characterizes the typical value of indicators

In an interval time series it is calculated as a simple arithmetic mean

In the moment dynamic series with equal time intervals between samples as a chronological average

2. Average absolute increase
A general indicator of the rate of absolute change in the values ​​of a time series

3. Average growth rate
Generalizing characteristics of growth rates of a series of dynamics

(root of degree i - 1)

4. Average growth rate
The relationship is the same as between growth rate and growth rate

All derivatives and averages shown here are calculated in the calculator (see below) as the user enters the series values ​​into the table.

On their personal page, registered users can save the calculator and remember the values ​​​​entered into it for reuse.

Momentary Interval

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Series values

Series values

(Tr) is an indicator of the intensity of changes in the level of a series, which is expressed as a percentage, and the growth coefficient (Kr) is expressed in shares. Kr is defined as the ratio of the subsequent level to the previous one or to the indicator taken as the basis of comparison. It determines how many times the level has increased compared to the base level, and in the case of a decrease, what part of the base level is being compared.

We calculate the growth rate, multiply by 100 and get the growth rate

Can be calculated using the formulas:

Also, the growth rate can be determined as follows:

The growth rate is always positive. There is a certain relationship between the chain and base growth rates: the product of the chain growth coefficients is equal to the base growth rate for the entire period, and the quotient of dividing the subsequent base growth rate by the previous one is equal to the chain growth rate.

Absolute increase

Absolute increase characterizes the increase (decrease) in the level of a series over a certain period of time. It is determined by the formula:

where уi is the level of the period being compared;

Уi-1 - Level of the previous period;

Y0 is the level of the base period.

Chain and basic absolute increases are related each other in this way: the sum of successive chain absolute increases is equal to the base, i.e., the total increase for the entire period of time:

Absolute increase can be a positive or negative sign. It shows how much the level of the current period is higher (lower) than the base one, and thus measures the absolute rate of growth or decline in the level.

(Tpr) shows the relative magnitude of the increase and shows by what percentage the compared level is greater or less than the level taken as the basis of comparison. It can be either positive or negative or equal to zero, it is expressed in percentages and shares (growth rates); is calculated as the ratio of absolute growth to the absolute level taken as the base:

The growth rate can be obtained from the growth rate:

The growth rate can be obtained as follows:

Absolute value of 1% increase

The absolute value of 1% growth (A%) is the ratio of absolute growth to the growth rate, expressed as a percentage and shows the significance of each percentage of growth over the same period of time:

Absolute value of one percent increase equal to one hundredth of the previous or base level. It shows what absolute value is hidden behind the relative indicator - one percent increase.

Examples of calculations of dynamics indicators

Before studying the theory on the topic of dynamics indicators, you can look at examples of problems on finding: growth rate, growth rate, absolute growth, average dynamics

About dynamics indicators

When studying the dynamics of social phenomena, the difficulty arises in describing the intensity of change and calculating the average indicators of dynamics that are asked to students.

Analysis of the intensity of change over time occurs using indicators that are obtained by comparing levels. These indicators include: growth rate, absolute growth, absolute value of one percent growth. To generalize the dynamics of the phenomena under study, the following are determined: the average levels of the series and the average indicators of changes in the levels of the series. Dynamics analysis indicators can be determined using constant and variable comparison bases. Here it is customary to call the comparable level the reporting level, and the level from which the comparison is made is the base level.

For calculation dynamics indicators on a permanent basis, you need to compare each level of the series with the same basic level. As a base level, only the initial level in the dynamics series or the level from which a new stage in the development of a phenomenon begins is used. The indicators that are calculated in this case are called basic. To calculate dynamics analysis indicators on a variable basis, you need to compare each subsequent level of the series with the previous one. The calculated dynamics analysis indicators will be called chain indicators.

In various areas of social life, a number of sciences and research methods, formulas for growth rates and growth rates are used. They are most often used in economics and statistics to identify trends and results of activities. This article discusses situations where these formulas are needed, their definitions, and how they are calculated.

Growth rate

Calculating the growth rate begins with defining a series of numbers between which you need to find a percentage relationship. The control number is usually compared either with the previous indicator or with the base number at the beginning of the number series. The result is expressed as a percentage.

The growth rate formula is as follows:

Growth Rate = Current/Baseline*100%. If the result is more than 100%, growth is noted. Accordingly, less than 100 is a decrease.

An example is the option of increasing and decreasing wages. The employee received a monthly salary: in January - 30,000, in February - 35,000. The growth rate was:

Rate of increase

The growth rate formula allows you to calculate the percentage of how much the value of an indicator has increased or decreased over a certain period. In this case, a more specific figure is visible, allowing one to judge the efficiency of work over time. That is, by calculating the ratio of wages (or other characteristic) using the growth rate formula, we will see by what percentage this amount has changed.

There are two calculation options:

1. Growth rate = current value / base value * 100% - 100%:

35 000/30 000*100%-100%=16,66%;

1. Growth rate = (current value - base value) / base value * 100%:

(35 000-30 000)/30 000*100%=16,66%.

Both calculation methods are identical. A negative mathematical result indicates a decrease in the indicator for the period under review. In our example, the employee’s salary in February was 16.66% higher than in January.

Formulas for growth and gain: basic, chain and average

The rate of growth and increment can be found in several ways, depending on the purpose of the calculation. There are formulas for obtaining basic, chain and average growth and increment rates.

Base rate of growth and gain shows the ratio of the selected series indicator to the indicator taken as the main one (calculation base). Usually it is at the beginning of the row. The formulas for calculation are as follows:

• Growth rate (B) = Selected indicator/Baseline indicator*100%;
• Growth rate (B) = Selected indicator/Base indicator*100%-100.

Chain rate of growth and gain shows the change in the indicator over time along the chain. That is, the difference in time between each subsequent indicator and the previous one. The formulas look like this:

• Growth Rate (G) = Selected Indicator/Previous Indicator*100%;
• Growth rate (G) = Selected indicator / Previous indicator * 100% -100.

There is a relationship between chain and base growth rates. The ratio of the result of dividing the current indicator by the base one to the result of dividing the previous indicator by the base one is equal to the chain growth rate.

Average growth and gain rate used to determine the average change in indicators for a year or other reporting period. In order to determine this value, you need to determine the geometric mean of all indicators in the period or find it by determining the ratio of the final value to the initial one:

Nuances of calculations

The formulas presented are very similar and can cause confusion and confusion. To do this, let us explain the following:

• the growth rate shows what percentage one number is of another;
• the growth rate shows by what percentage one number has increased or decreased relative to another;
• the growth rate cannot be negative, the growth rate can;
• the growth rate can be calculated on the basis of the growth rate; the reverse order is not allowed.

In economic practice, the growth indicator is more often used, since it more clearly reflects the dynamics of change.

In contact with

Growth and growth rates are calculated very often, and not only in statistics, but also in economics, manufacturing and even sociology and law, and every student is faced with the task of understanding what these indicators are, how they are calculated and how they differ. Often students begin to get confused about them, let's try to prevent this.

Growth rate– a relative economic indicator showing the percentage growth of one indicator over the same indicator of the previous period.

For example, using the growth rate, you can calculate what your salary this year was as a percentage compared to last year.

If the result is more than 100, there is an increase; if less than 100, there is a decrease.

Example No. 1.1 The average wage of a worker in 2016 was 33,000 rubles, and in 2015 it was 31,500 rubles; let’s calculate the growth rate based on the given conditions. You can find out more about how to calculate the growth rate.

Growth rate = 33000/31500 * 100 - 100 = 104.76-100 = 4.76%. Thus, the average salary increased by 4.76% (+4.76%).

Example No. 2.2

Growth rate = 139000/142000 *100 -100 = 97.89-100 = -2.11%. The value turned out to be negative, which means the rate of decline in profit was 2.11%, or, more simply put, the profit of the reporting year decreased by 2.11% compared to the profit of 2015.

How else can you calculate the growth rate?

If in the task you calculated the absolute deviation, then you can use this value and divide it by the value of the base year, consider example No. 1.1

Absolute deviation = 33,000 – 31,500 = 1,500 rubles.

Growth rate = 1500 / 31500 * 100% = 4.76%. We see that changing the calculation method left the result unchanged, so choose the method that you like best.

Let's return to the topic of the article and summarize what the difference is between the growth rate and the growth rate. The difference between the indicators is as follows:

1. Calculation method.
2. The growth rate shows what percentage one indicator is relative to another, and the growth rate tells how much it has grown.
3. The growth rate is calculated based on the growth rate, but not vice versa.
4. The growth rate cannot be negative, and the growth rate can be both positive and negative.

If, after reading the material, it is not clear to you how to calculate the indicator or you still have questions on the topic, do not hesitate to ask them in the comments.