Statistics 8th Edition Jia Junping Chapter 14 summary of index knowledge points and answers to exercises after class

Catalog

One 、 Knowledge framework

Two 、 After-school exercises

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One 、 Knowledge framework

Two 、 After-school exercises

1 An enterprise produces a 、 B two products , The data is shown in the table 1 Shown .
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requirement ：
（1） Calculate the individual index of output and unit cost .
（2） Calculate the total output index of the two products and the increased production costs due to the increase in output .
（3） Calculate the total index of unit cost of two products and the production cost saved due to cost reduction .

Explain ：（1） Individual index of output and unit cost
The output index of product a is ：Iq nail ＝q1 nail /q0 nail ＝2200/2000＝110.00%;
The unit cost index of product a is ：Ip nail ＝p1 nail /p0 nail ＝12.5/12.0＝104.17%;
The output index of product B is ：Iq B ＝q1 B /q0 B ＝6000/5000＝120.00%;
The unit cost index of product a is ：Ip B ＝p1 B /p0 B ＝6.0/6.2＝96.77%.
（2） Total output index of two products
The calculation result of Laplace production index is ：

The increased production cost due to the increase in production is ：
∑p0q1－∑p0q0＝（2200×12.0＋6000×6.2）－（2000×12.0＋5000×6.2）＝8600（ element ）
（3） Total index of unit cost of two products
The calculation result of Pascal's unit cost index is ：

The cost savings due to cost reduction are ：
∑p0q1－∑p1q1＝（2200×12.0＋6000×6.2）－（2000×12.5＋6000×6.0）＝100（ element ）2 The data of three kinds of goods sold in a shopping mall are shown in the table .

requirement ：
（1） Calculate the total sales index of three commodities .
（2） Analyze the absolute and relative values of the impact of sales volume and price changes on sales .

Explain ：（1） The total sales index of the three commodities

（2） Absolute value of sales change
∑p1q1－∑p0q0＝（115×100＋220×55＋315×25）－（100×100＋200×50＋300×20）＝5475（ element ）

① Impact analysis of sales volume changes ：

The absolute amount affected by the change in sales volume is ：∑p0q1－∑p0q0＝28800－26000＝2800（ element ）.

② Analysis of the impact of sales price changes ：

The absolute amount affected by the change of sales price is ：∑p1q1－∑p0q1＝31475－28800＝2675（ element ）.
The results show that , In terms of relative numbers , The sales volume of the shopping mall increased in the reporting period compared with the base period 21.06%, It is due to the increase in sales 10.77% And sales price growth 9.29%, The result of the joint action of these two factors ; In terms of absolute numbers , The sales volume of the shopping mall increased in the reporting period compared with the base period 5475 element , It is because the sales volume increases 2800 The rise of yuan and sales price increases sales 2675 element , The result of interaction .

3 Try to calculate the sales volume index and price index by using Laplace index and Paasche index respectively according to the table .

Explain ： The calculation result of La sales index is ：

The calculation result of Paasche sales index is ：

The calculation result of the LaSalle price index is ：

The calculation result of Paasche price index is ：

4 The relevant information of three products of a company is shown in the table , How much has the output of the three products increased on average ？ What is the impact of output growth on output value ？

Explain ：

therefore , The output of the three products increased on average 25.00%. In terms of relative quantity , The output growth has increased the output value 25%, In absolute terms , The increase in output has increased the output value 65 Ten thousand yuan .

5 The sales data of the three commodities are shown in the table , Explain the total change of its price through calculation .

Explain ：

in general , The selling prices of the three commodities are lower than the base period 1－87.78%＝12.22%.

6 The sales revenue of a shopping mall in the last period was 525 Ten thousand yuan , The requirements of this period are 556.5 Ten thousand yuan . Reduce the specified sales price 2.6% Under the condition of , How much will the sales volume of the store increase , In order to make the current sales reach the original target ？ Explain ： The total sales index is ：I＝∑p1q1/∑p0q0＝556.5/525＝106%;
The known price index is ：1－2.6%＝97.4%;I＝Ip×Iq;
Then the sales volume index is ：Iq＝I/Ip＝106%/97.4%＝108.83%;
Therefore, the sales volume of goods in this store should increase 8.83%, In order to make the current sales reach the original target .

7 A region 2003 The annual average number of employees is 229.5 ten thousand people , Than 2002 Increase in 2%;2003 The total annual salary is 167076 Ten thousand yuan , Than 2002 Annual expenditure 9576 Ten thousand yuan . Try to calculate 2002 The average annual salary of employees .

Explain ：2002 The average annual salary of employees is ：

8 An electronic manufacturing enterprise 2003 Years and 2002 The unit cost and output data of the three main products in are shown in the table

requirement ：
（1） Calculate the total output value index and the total increase or decrease of output value of the three products .
（2） With 2003 Calculate the weighted unit product cost comprehensive index of the three products with the annual output as the weight , And the increase or decrease in output value due to changes in output .
（3） With 2002 The annual unit product cost is the weight to calculate the weighted output composite index of the three products , And the increase and decrease of output value due to the change of unit product cost .
（4） Analyze the relative value and increase and decrease of the impact of changes in output and unit product cost on sales .

Explain ：（1） The total output value index of the three products is ：

The total increase or decrease in output value is ：
∑p1q1－∑p0q0＝（9×1000＋58.5×500＋115×800）－（8.5×900＋55×500＋100×700）＝25100（ element ）
（2） With 2003 The comprehensive index of weighted unit product cost of the three products calculated with the annual output as the weight is ：

The increase or decrease of output value due to the change of unit product cost is ：
∑p1q1－∑p0q1＝（9×1000＋58.5×500＋115×800）－（8.5×1000＋55×500＋100×800）＝14250（ element ）
（3） With 2002 The annual unit product cost is the weight, and the weighted output composite index of the three products is ：
The increase or decrease in output value due to changes in output is ：

∑p0q1－∑p0q0＝（8.5×1000＋55×500＋100×800）－（8.5×900＋55×500＋100×700）＝10850（ element ）
（4） Total increase or decrease in output value ＝ The impact of output changes on output ＋ The impact of changes in unit product costs on output , namely
∑q1p1－∑q0p0＝（∑q1p0－∑q0p0）＋（∑q1p1－∑q1p0）
comprehensive （1）（2）（3） It can be seen that , The rise in the cost of unit products has increased the output value 12.28%, The increase is 14250 element ; The increase in output has increased the output value 10.32%, The increase is 10850 element .

9 There are three production workshops in a factory , The number of employees and labor productivity data of each workshop in the base period and the reporting period are shown in the table . Try to analyze the change of labor productivity of the enterprise and its reasons .

Explain ： The average labor productivity in the base period is ：x0＝∑x0f0/∑f0＝（4.4×200＋6.2×160＋9.0×150）/510＝6.32（ Ten thousand yuan / people ）
The average labor productivity in the reporting period is ：x1＝∑x1f1/∑f1＝（4.5×240＋6.4×180＋9.2×120）/540＝6.18（ Ten thousand yuan / people ）
Assume that labor productivity remains unchanged , The average labor productivity of the enterprise is ：xn＝∑x0f1/∑f1＝（4.4×240＋6.2×180＋9.0×120）/540＝6.02（ Ten thousand yuan / people ）
Analysis on the change of the average labor productivity of the enterprise ：
Total average level index ：
Ixf＝x1/x0＝6.18/6.32＝97.79%
Changes in labor productivity ：x1－x0＝6.18－6.32＝－0.14（ Ten thousand yuan / people ）
among ：
（1） The impact of changes in the labor productivity of the three workshops on the average labor productivity
Group level change index ：
Ix＝x1/xn＝6.18/6.02＝102.58%
The impact of changes in the labor productivity of each workshop on the labor productivity of the whole plant ：x1－xn＝6.18－6.02＝0.16（ Ten thousand yuan / people ）
（2） The impact of changes in the number of workers in each workshop on labor productivity
Structural change index ：
If＝xn/x0＝6.02/6.32＝95.32%
The impact of changes in the number of people in each workshop on the labor productivity of the whole plant ：xn－x0＝6.02－6.32＝－0.3（ Ten thousand yuan / people ）
The results show that , The average labor productivity of the whole plant decreased 2.21%, among , The improvement of labor productivity in each workshop will increase the labor productivity of the whole plant 2.58%, Changes in the structure of the number of people in each workshop have reduced the labor productivity of the whole plant 4.68%, namely
97.79%＝102.58%×95.32%
In absolute numbers , The labor productivity of the whole factory has decreased 0.14 Ten thousand yuan / people , among , The improvement of labor productivity in each workshop will increase the labor productivity of the whole plant 0.16 Ten thousand yuan / people , Changes in the structure of the number of people in each workshop have reduced the labor productivity of the whole plant 0.3 Ten thousand yuan / people , namely －0.14＝0.16＋（－0.3）.

10 surface 14-9 It's somewhere 2005 Simple table for calculation of annual grain retail price index , Please use the information in the table , Explain the general steps of compiling commodity retail price index , And calculate 2005 Annual grain retail price index .

Explain ：（1） Calculate the price index of each representative specification
The price index of flour ：i＝p1/p0＝2.20/2.00＝110.0%;
The price index of Japonica rice ：i＝p1/p0＝3.00/2.80＝107.14%.
（2） According to the price index of each representative specification and the corresponding weight given , Calculate the sub category index by using the weighted arithmetic average
Price index of fine grain ：
ip＝∑iW/∑W＝（1.10×56＋1.0714×44）/100＝108.74%
（3） According to the indexes of each sub category and the corresponding weights , The weighted arithmetic average calculates the general index
Grain price index ：
ip＝∑iW/∑W＝（108.74%×82＋104.18%×18）/100＝107.92%