大三上統(tǒng)計(jì)學(xué)index

1、1Chapter4 Statistical IndexSTATKey points1、The conception and the type of index number；2、Drawing of index number；3、Index system and factor analysis ；4、Some economic indexes in true-life。Difficulties1、The drawing principle of qualitative index 、quantitative index；2、The differences among aggregate ind

2、ex、mean value index and average target index。2Chapter4 Statistical IndexSTAT4.1 The Conception and Type of Statistical Index4.1.1、Index Number1、The Origin of Index Number：in 1650,Rice Voughan (English) initiated a kind of Stat analyzing method。 e.g. 1700 1710 Price of bread： 1penny/piece 1.2penny/pi

3、ece 1.2/1=120%2、The broad definition of index number：relative numbers that reflect the change of phenomenal quantity 。（1）first “dynamic change”;（2）thereafter “space change”； region A region Bpopulation： 1 million 0.8 million 100/80=125%（3）today all of the relative numbers。3Chapter4 Statistical Index

4、STAT3、The narrow definition of index number：the relative numbers that reflect the quantity change of difficult phenomenal population.（1）Difficult phenomenal populationunit numbers and quantity characters cant be added directly.The sale of a market： Q0（1999） Q1（2000）TV (set ) 12,000 15000 1.5/1.2=125

5、%Slipper (pair) 50,000 40,000 4/5=80%Robust (bottle) 200,000 300,000 30/20=150%（2）quantity index；（3）change: base period reporting period；（4）relative number dynamic relative number：reflect the changing direction and degree of phenomenal quantity. 4Chapter4 Statistical IndexSTAT4.1.2、Classification of

6、 index number1、According to the different range of reflection. （1）Individual Index：the relative number which reflects the quantity change of single economic phenomenon.individual index of sales priceIndividual index of sales quantityUnit: ten thousand kilograms yuan5Chapter4 Statistical IndexSTAT（2）

7、Total Index：Relative numbers that reflect the quantity change of difficult phenomenal population.（3）Index of class：relative numbers that reflect the quantity change of certain phenomenal population.Unit: ten thousand kilograms yuan6Chapter4 Statistical IndexSTAT2、According to different characters of

8、 index（1） quantitative index ：relative numbers that reflect the change of quantity target (q).（2） qualitative index ：relative numbers that reflect the change of quality target (p).3、According to the phenomenal reflection in different time and status.（1）dynamic index dynamic relative numbers；（2）stati

9、c index other relative numbers。4、According to different ways of calculating, general index aggregate index、mean value index。7Chapter4 Statistical IndexSTAT4.2 Aggregate Index4.2.1: Definition: first integrate(+)、then contrast()total index。4.2.2 Drawing of Index（1）general change index（2）quantitative

10、index（3）qualitative index （4）aggregate index system e.g. The data of three goods in a supermarket (unit: yuan, 10 thousand kilogram）8Chapter4 Statistical IndexSTATCalculate：（1）The aggregate changing degree of sales of these three goods and the change of moneyanalyze sales change of one good：p0q0 p1q

11、1； the aggregate change of sales of three goods：p0q0 p1q1；9Chapter4 Statistical IndexSTAT4.2.2.1 Total change IndexMethod：first integrate、then contrast aggregate index。10Chapter4 Statistical IndexSTAT（2）Please try to calculate the aggregate changing degree of sales quantity of these three goods and

12、the change of money.analysis sales of goods (p q)=sales quantity (q) sales price (p) the aggregate change of sales of these three goods: 11Chapter4 Statistical IndexSTAT4.2.2.2 Quantitative IndexWeighted factors：the medium that transfer different un-weighted factors into weighted factors12Chapter4 S

13、tatistical IndexSTAT13Chapter4 Statistical IndexSTATExplain Though the change of sales quantity of three goods are not the same, but in total, the sales quantity of three goods have raised 15.88%，which has raised the sales by 277,500yuan。Note: weighted factors unchangeable factor；indexation factors

14、changeable factor。14Chapter4 Statistical IndexSTAT（3）Try to calculate the aggregate changing degree of sales price of these three goods and the change of money.Analysis change of price of one goods：p0p1； the aggregate change of price of three goods：p0 p1；e.g. The data of three goods in a supermarket

15、 (unit: yuan, 10 thousand kilogram ） good p0 p1 q0 q1 kp(%) kq(%) ccucumber tomato potato 2.2 2.0 0.65 1.6 1.8 0.72 45 20 55 50 30 50 72.73 90 110.77 111.11 150 90.91 15Chapter4 Statistical IndexSTAT4.2.2.3 Qualitative Index 16Chapter4 Statistical IndexSTATprice：people emphasize particularly on its

16、real economic signification. 1this year、0 last year。17Chapter4 Statistical IndexSTATPrinciple of drawing the qualitative index：use Pacsche Index to draw。Explain：Although the changes of price of these three goods are not the same, but in total, the price of three goods had decreased 16.05%，which has

17、reduced the sale by 325,000 yuan.18Chapter4 Statistical IndexSTAT4.2.2.4 Aggregate Index System 1、Index System：An integer formed by three or more than three indexes which has some relationships of economy, equity connections of quantity.A、the relations of economy sale of goods=sales quantity sales p

18、rice total production value=production price （p q）production of crops=unit area outputplanting area (p q)B、equity of quantityEquity of relative numberEquity of absolute number19Chapter4 Statistical IndexSTAT2、factor analysisProcess：from right to left, from relative number to absolute number.（1）compa

19、re with the base year, the sales quantity of three goods has increased 15.88% in reporting year, bring an increase of sale of 277,500yuan factor analysis;（2）compare with the base year, the sales price has decreased 16.06%,the sale has decreased 325,000yuan factor analysis;（3）the two factors affect t

20、ogether, the sales has decreased 2.72% compared with the base year, which is 47,500yuan factor analysis.Unit: ten thousand yuan20Chapter4 Statistical IndexSTAT3、the effect of index system（1）factor analysis；（2）determine the period of the weighted factors；The first index systemThe second index system2

21、1Chapter4 Statistical IndexSTAT（3）the calculation of unknown indexe.g. Compare with the base year, employee number has increased2% until reporting year，total production has increased 20%，asking the change of total labor productivity？Solution：find the relationships between indexes Total production va

22、lue=amount of employees total labor productivitysymbolic： p q = q p22Chapter4 Statistical IndexSTAT4.3 Mean Value Index4.3.1The disadvantages of Aggregate Index1、obtain data：p1q1 ,p0q0easy，p0q1 difficult；2、workload of calculation and data collection：If it needs to reflect the aggregate change about

23、price or sales amount of many goods very huge。4.3.2、The conception of mean value index1、definition: use the way of calculating mean value to calculating the total index。2、type:（1）transformative aggregate index ；（2）independent formal of mean value index。23Chapter4 Statistical IndexSTAT4.3.3、 Transfor

24、mative Aggregate Index (Mean value index)1、general index of sales（general changing index）24Chapter4 Statistic IndexSTAT2、general index of sales amount（ Quantitative Index ）weighted arithmetic average index25Chapter 4 Statistic IndexSTAT3、aggregate index of sales price（qualitative index）weighted harm

25、onic mean index26Chapter 4 Statistic IndexSTAT4、mean value index system27Chapter 4 Statistic IndexSTAT4.4 Average Target Index4.4.1 definition： relative numbers obtained from the contrasting of weighted arithmetic mean value in two period28Chapter 4 Statistic IndexSTAT(factor analysis)29Chapter 4 St

26、atistic IndexSTAT4.1.2 the type of average target index1、variable structure index（the distortion of general variable index）30Chapter 4 Statistic IndexSTATanalysis because of average wage per month and population structure change together，the general average wage decreases 1.72%，the average wage per

27、person decreases 10yuan, the factory wage expenditure decreases 10000yuan。 31Chapter 4 Statistic IndexSTAT2、fixed structure index（the distortion of quality target index）32Chapter 4 Statistic IndexSTATanalysis exclude the structure change of the workers, pureness because of the affect of the average

28、wage per month，the general average wage per month increase 9.62%，per person gains 50yuan more ，the factory wage expenditure increases 50000yuan 。33Chapter 4 Statistic IndexSTAT3、structure affect index（the distortion of quantity target index）34Chapter 4 Statistic IndexSTATanalysis exclude the change

29、of average wage per month , pureness because of the affection of the population structure ，the general average wage decrease10.34%，per person gains 60yuan less than before,，the factory reduces wage expenditure 60000yuan。35Chapter 4 Statistic IndexSTAT4、average target index system36Chapter 4 Statisti

30、c IndexSTATanalysis Exclude the change of average wage per month ，pureness due to the change of the population structure，the general average wage decreases 10.34%，per person gets 60yuan less than before； Exclude the alternation of the population structure ，because of the affection of average wage pe

31、r month，general average wage increases 9.62%，per person gains 50yuan more than before。 The affection of the two factors work together, the general average wage drops1.72%，per person gets 10yuan less than before.37Chapter 4 Statistic IndexSTAT4.5 Multi-factor Index System4.4.1 Definition Profit tax a

32、mount =Sales Profits and taxes rate =Sales volume sales price Profits and taxes rateqmp = q m p4.5.2 Drawing principle1、Quantitative index at the front, qualitative index after；2、The neighboring two targets product must have the actual economic significance；3、When analyzes the influence of some fact

33、ors, the various factors behind fix in the base period level, the various factors in front fix in thecurrent period level38Chapter 4 Statistic IndexSTATe.g qmp = q m p39Chapter 4 Statistic IndexSTAT4.6 Economic Index in Reality Question proposing 1、aggregate indexes and mean value indexes，it needs t

34、o collect the comprehensive material when drawing them, and it faces very big limitations in the practical application.2、the method of improvement40Chapter 4 Statistic IndexSTAT4.6.1 Retail price index1 . Definition: retail price index is an economic index reflects retail price change tendency of th

35、e city and countryside commodity 。2. The steps of drawing retail price index（1）the choice of research area and point, represents the specification on behalf of the commodity choice,（2）the choices of representative commodity and representative standard sample.Selection principle The sales quantity (a

36、mount) is big; market supplies maintain stable; price changing tendency hasrepresentation; there have big differences between representative standard sample; have close relations with social produce and thelives of people.（3）way of price investigation;（4）weight determination.41Chapter 4 Statistic In

37、dexSTAT4.6.2 Consumer price index1、definition：reflect the price change index that residents buying consumables and obtain services in a certain period. 2、consumer price index and retail price index are the same, the differences are CPI contains consume price and service price, its weight is defined

38、with the structure of family consumer expenditures of residents.3、CPI not only reflect the price change tendency and degree that residents buying consumables and obtain services in a certain period, it also have other uses:（1）reflect the status of inflation42Chapter 4 Statistic IndexSTAT（2）use to re

39、flect the changes of purchasing power of currency（3）use to reflect the influences of real wages of staffs43Chapter 4 Statistic IndexSTAT4.6.3、producer price index（PPI）1、definition：producer price index is a price index that measure the changes of price in primary markets. (the first transaction of so

40、me products in non retail markets)。2、one of the common use of PPI is as a leading indicator of the future trend of consumer prices and the cost of living. An increase in the PPI reflects producer price increases that will eventually be passed on to the consumer through higher retail prices。3、the PPI

41、 is published by month。44Chapter 4 Statistic IndexSTAT4.6.4 Stock price index1、definition; stock price index is the relative number that reflects stocks price change in a certain stock market, abbreviate stock price index, its unit generally uses “point to express.。2、calculate the stock price indexA

42、t present，there are plenty of methods to calculate SPI，but usually we use circulation serve as weight number to calculate the weighted aggregate.。The formula is ； In the formula: is the current period price of ith kind of sample stock, is the base period price of ith kind of sample stock, ith kind s

43、tock circulation, which can determine the current period also may be the base period, but mostly is the current period45Chapter 4 Statistic IndexSTATThe Dow Jones averages are indexes designed to show price trends and movements on the New York Stock Exchange。The best known of the Dow Jones indexes i

44、s the Dow Jones Industry Average (DJIA), which is based on common stock prices of 30 large companies, it is the sum of these stock prices divided by a number, which is revised from time to time to adjust for stock splits and switching of companies in the index. Unlike the other indexes that we have studied, it is not expressed as a percentage of base-year prices. 46Chapter 4 Statistic IndexSTATExercise1、A factorys output in current period increases 5% compared to the base period, the cost per unit of output falls 5%, then this factory total cost does not increase and does not reduce。（ ）key：f