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# Business statistics and forecasting

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**28.08.2013**

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## Description

Individual work on the course

"Business Statistics and forecasting."

(Laboratory practical and four current control)

K = 1

Number 1 "Average, average structure, indicators of variations."

Calculations carried out with an accuracy of two decimal places.

According to Table 1 on the distribution of the company's employees by wage levels required to determine:

• Average salary ()

• mode (Mo),

• the median (Me),

• standard deviation,

• coefficient of variation (V).

Give an interpretation of the results.

Table 1. Distribution of employees by size of firm wage

Monthly wages (Rub.)

Number of employees (fi)

(18000 + 100) and at least

9

(100 + 18000) - (21000 + 100)

21

(100 + 21000) - (24000 + 100)

30

(100 + 24000) - (27000 + 100)

25

(27000 + 100) - (30,000 + 100)

10

over (30,000 + 100)

5

Total 100

Number 2 "Key performance indicators".

Calculations were carried out with an accuracy of one decimal place.

On the basis of the profit of the company for five years (thous.) To calculate the required chain, basic and secondary:

a) absolute increases;

b) the growth rate;

c) growth rates.

As a baseline, take entry-level series.

Give an economic interpretation averages.

Calculate the forecast by the average absolute increase and the average growth rate for the year ahead. Make a conclusion about the correctness of the use of these approaches to predict the dynamics of this indicator. (Justify your conclusion).

Table 2. Dynamics of the company's profits

Number, the company's profit

T Yt (thous.)

+ 1 175 to

2181 + to

3185 + to

4190 + to

5194 + to

№3 «The use of models of growth curves in economic forecasting"

Calculations carried out with an accuracy of two decimal places.

Available quarterly data for the profit of the company (thous.).

Table 3. Dynamics of the company's profits

t yt (thous.) t yt (thous.) t yt (thous.)

1 80.4 6 115.2 + K + K + K 11 147.4

2 TO 7 + 88.3 118.4 155.2 + 12 K + K

3 TO 8 + 92.0 127.1 169.8 + 13 K + K

4 98.5 + K + K 9 131.3 14 176.7 + K

5 109.9 10 136.9 + K + K + K 15 192.4

Assuming that the trend can be described as a series of linear model to determine the coefficients of the model using the method of least squares (OLS). To simplify the calculations, do the transfer of the origin in the middle of a number of speakers. Calculate using the constructed model point forecast for the period of pre-emption L = 1.

Monitoring №1

1. Determination of optimal number of groups based on a formula Sturgess, which is as follows:

a) K = 1 + 3,322lgN; b);

c); g) A = 1 * 3,322lgN.

2.Velichina groups of equal interval is determined by the formula:

a) h = 1 * 3,322lgN; b) h = (Xmax-Xmin) * K;

a) h = (Xmax-Xmin) / K; g) h = 1 + 3,322lgN.

3.Formula arithmetic mean can be as follows:

a); b);

c); g).

4. If all of the options to increase the tag 10, the arithmetic average:

a) increase by 10 times; b) decreased by 10 times;

c) increase by 10; d) will decrease by 10.

5. If the weight increase 2 times, the average value;

a) does not change; b) reduced 2-fold;

c) increased by 2 times; d) will decrease by 10.

Monitoring №2

1.Sredny individual values \u200b\u200bof the square is equal to 88, the dispersion characteristic

-52. The value of the average value equal to:

a) 6; b) 36;

c) 140; d) 44.

2. The coefficient of variation of the characteristic is 25%, the average value of feature -20. The dispersion characteristic is:

a) 25; b) 36;

c) 140; d) 44.

3.Koeffitsient trait variation is 50%, the dispersion characteristic -3600. The average value of the flag is equal to:

a) 25; b) 36;

c) 120; d) 44.

## Additional information

4. On the data on the distribution of banks in the amount of loans issued, determine the value of the median.

The amount of loans issued by banks,

mln.d.ed. 20-40 40-60 60-80 80-100 100-120

The number of banks

6 10 14 11 9

The median is:

a) 72.9; b) 60;

c) 82; d) 44.

5.Po data on the distribution of banks on loans to customers define value fashion.

The amount of loans issued by banks, mln.d.ed.

20-40

40-60

60-80

80-100

100-120

The number of banks

June 14 11 10 9

Fashion is:

a) 72.9; b) 54.5;

c) 82.3; r) 40.0.

Monitoring №3

1.Tendentsiya changes in the average annual number of industrial production personnel described by the model of the enterprise:. According to the model the average growth rate of population was as follows:

a) 2.2%; b) 31%; c) 22%; g) 12.2%; d) 102.2%.

2.Godovaya dynamics of the company's profit model is described:

According to the model, the average annual growth of profit is:

a) 6.4 [thousand.] b) -6.4 [thousand.] c) 372.2 [thousand.] g) 72.2 [thousand dollars].

3.Ezhekvartalnaya dynamics of the interest rate of the bank for 5 quarters is presented in the table below:

t 1 2 3 4 5

yt,% 7,3 8,8 9,7 10,7 8

The forecast of the interest rate of the bank at 6 quarter, calculated using the average growth rate is equal to:

a) 11.1%; b) 11.8%; a) 10, 9%; g) 11.5%; d) 11.6%.

4.Urovni time series vary from approximately constant growth rate. Prediction one step forward using the average growth rate can be calculated by the formula:

a); b); c); g).

5.Dinamika time series is close to a linear development. Prediction two steps forward by the average of the absolute gain can be calculated using the formula:

a); b); c); g).

Monitoring №4

1. Introduction levels of time series (t = 1,2, ..., n) as:

Where ut -trendovaya component; cyclic component; st-seasonal component; a random component that corresponds to the model:

a) the multiplicative; b) an additive; c) mixed type; d) an adaptive

2. Presentation of levels of the time series (t = 1,2, ..., n) as: where ut-trend component; cyclic component; st-seasonal component; a random component that corresponds to the model:

a) the multiplicative; b) an additive; c) mixed type; d) adaptive.

3. For a description of periodic oscillations with a period of three months is used:

a) the seasonal component; b) random component;

c) the trend component; d) cyclical component.

4.Predstavlenie levels of the time series (t = 1,2, ..., n) as:

Where ut -trendovaya component; cyclic component; st-seasonal component; a random component that corresponds to the model:

a) the multiplicative; b) an additive; c) mixed type; d) an adaptive

5. For the description of periodic oscillations with a period of five years is used:

a) the seasonal component; b) random component;

c) the trend component; d) cyclical component.

Laboratory workshop.

Number 1 "Average, average structure, indicators of variations."

Table 1.1. Auxiliary calculations (calculation of descriptive statistics).

Monthly wages (Rub.)

Number of employees (fi) Cumulative frequency

(FiN) Mid-range

(Xi) xi * fi

18200 and less than 9 September 16600 149 400 395 612 100

18200 - 21200 21 30 19 600 411 600 276 714 900

21200 - 24200 30 22600 60 678000 11907000

24200 - 27200 25 85 25 600 640 000 140 422 500

.....

The summation in formulas when calculating A0 and A1 is carried out in t, obtained after migration of the origin in the middle of the time series (ie, t: -7, -6 ... .0 ... ..6,7). For the forecast profit in the next quarter should be taken t = 8.