1、Statistics in Practice,STAT,Statistics in PracticeCouple of years ago, a film called Dont bother me after divorced became quite famous, both with the topic and acting. In Jan. 2003, there was a news on the social news page of a newspaper, which titled Still get to you after divorced. The news was ab
2、out the rising fee of a single-parent children in a divorce family.In the news, Mr. Fu and Ms. Zhang divorced in Nov. 1986. After the divorce, the child was to live with the mother. The father was judged to pay a alimony of 17 Yuan every month. But afterwards, because of the inflation, the life of t
3、he plaintiff gets harder. Hence through 4 suits in 1990, 1994, 1995 and 1996, the alimony was risen to 30, 50, 70 and 90 Yuan. From a statistical point of view, what method did the judge used when redetermining the alimony?,Statistics in Practice,STAT,Today, not only alimony for divorced couples, bu
4、t also pension for the retired; the determination of corruption; the standard of social security subsidy; the starting point of personal income tax and the payment of debts are using the methods of indexation.Through the learning of this chapter, we can understand the meaning and the calculation of
5、statistical indices, and the way of explaining the quantities changes in economic problems with the method of index analysis.,Chapter 5 Statistical index,STAT,Key points 1. The concepts and types of index numbers（P723）; 2. The compiling of index numbers; 3. The index systems and factor analysis; 4.
6、Some index numbers in practice。Difficulties 1. The principles in the making qualitative index（质量指标指数） and quantitative index（数量指标指数）; 2. The difference between aggregative index number（总指数）, mean index（平均数指数） and index numbers of average indicator（平均指标指数）.,Chapter 5 Statistical index,STAT,Section 1
7、The concepts and types of index 1. The concepts of index numbers（P723） 1) The origin of index number: A statistical analysis method first developed by an Englishman named Rice Voughan in 1650.Example 1709 1710 Bread price： 1 penny/piece 1.2 1.2/1=120% 2) Index number in broad sense（广义指数）: The relati
8、ve numbers that shows the numeric changes of phenomenon. (1) Initially “Dynamic change”; (2) Afterwards “Space change”；A B Population (2005) 100 80 100/80=125%,Chapter 5 Statistical index,STAT,3) Index number in narrow sense: The relative numbers that shows the numeric changes of the population of c
9、omplex phenomenon. Sales of a store：Q0 (2003) Q1 (2004) TV (set) 12000 15000 1.5/1.2=125% Slipper (pair) 50000 40000 4/5=80% Robust (bottle) 200000 300000 30/20=150% (1) Quantity Indicator (sales) (2) Changes: Base period Report period; (3) Relative number Development speed: To reflect the direction
10、 and degree of the numeric changes of phenomenon.,Chapter 5 Statistical index,STAT,2. Types of index numbers 1) Based on the range (1) Individual Index（个体指数）,Chapter 5 Statistical index,STAT,Section 2 Aggregate index numbers 1. Definition: First aggregate, then compare Total index number. 2. Making
11、(P723) 1) Total change index number（总变动指数）; 2) Quantitative index（数量指标指数）; 3) Qualitative index（质量指标指数）; Example 3 kind of items in a super market.,Chapter 5 Statistical index,STAT,(1) The total degree and the sum of change of sales of these three goods; Analysis Change of the sales of 1 item: p0q0
12、p1q1；Change of the sales of 3 items: p0q0 p1q1；,Chapter 5 Statistical index,STAT,3. Total change index number（总变动指数）,Method: First aggregate, then compare Aggregative index number（composite index，综合指数）.,Chapter 5 Statistical index,STAT,(2) Calculate the degree of changes of sale quantity for the 3 g
13、oods and the sum influenced by those changes. Analysis Sales (pq) = Sale quantity (q) sale price (p)The change of sale quantity for the 3 goods: q0 q1;,Chapter 5 Statistical index,STAT,4. Quantitative Index (P736),Unifying factor（同度量因素）: The medium factor that transfer the different measurement unit
14、s into a same measurement unit.,Chapter 5 Statistical index,STAT,Indexation factor: The changing factor,Unifying factor: The constant factor,Chapter 5 Statistical index,STAT,Question: In the two indices, which one can better (more purely) reflect the change of sale quantity?,The principle of making
15、quantitative index : Use Laspeyres index（“数拉基”）.,Chapter 5 Statistical index,STAT,(3) Calculate the degree of changes of sale prices for the 3 goods and the sum influenced by those changes. Analysis The change of the price of an item: p0p1；The overall change of prices of 3 items: p0 p1；,Chapter 5 St
16、atistical index,STAT,5. Qualitative Index (P725),Chapter 5 Statistical index,STAT,Price: The real economic meaning is what people are concerned with. 1This year, 0 Last year. If cov（p，q）0，LP. The principle of making qualitative index : Use Paasche index.,Chapter 5 Statistical index,STAT,6. Aggregati
17、ve index number system 1) Index number system: The system that was consisted of 3 or more indices, which are economically and numerically related. (1) Economically relatedSales = Sale quantity sale price(pq) Industrial product = Output Price (q p) Crop yield = Yield per area Planting area (2) Numeri
18、cally related,Chapter 5 Statistical index,STAT,2) Factor analysis,(1) The sale quantity of 3 goods have risen 15.88% in the report period comparing to the base period. This caused the sales to rise 27.75 thousand yuan. Sale quantity factor analysis; (2) The sale prices of 3 goods have dropped 16.05%
19、. This caused the sales to drop 32.5 thousand yuan. Sale price factor analysis; (3) As the result of the two factors combined, the sales dropped 2.72%, which translates to 4.75 thousand yuan. Total change analysis.,Chapter 5 Statistical index,STAT,3) Usage of index number system (1) Factor analysis;
20、 (2) Determine the period for unifying factor（数拉基，质派报）;,Chapter 5 Statistical index,STAT,(3) Estimation of unknown index numbers Example In a factory, comparing to the base period, the number of employees increased 2% in the report period, and the total product increased 20%. How did the productivit
21、y changed? Solution: Find out relations between indicatorsIndustrial product = Number of employees Productivity Symbolize: pq = q p,Chapter 5 Statistical index,STAT,Section 3 Mean index number 1. The problems of aggregative index number,1) Obtaining the data: p1q1; p0q0; p0q1. 2) The effort needed t
22、o calculate and obtain the data is massive. 2. The concepts of mean index number（平均数指数） 1) Definition: Using the method of mean Total index 2) Types (1) Mean index numbers that was transformed from aggregative index number（综合指数变形的平均数指数） (2) Independent (fixed weights) mean index numbers,Chapter 5 St
23、atistical index,STAT,3. Mean index that was transformed from aggregative index number,1) Total index of sales (Index number of total changes),Chapter 5 Statistical index,STAT,2) Total index of sale quantity (Quantitative index),Weighted arithmetic mean index numbers（加权算术平均数指数） that was transformed f
24、rom aggregative index number,Chapter 5 Statistical index,STAT,3) Total index of sale price (Qualitative index),Weighted harmonic mean index numbers（加权调和平均数指数） that was transformed from aggregative index number,Chapter 5 Statistical index,STAT,4) System of mean index that was transformed from aggrega
25、tive index,Chapter 5 Statistical index,STAT,Section 4 Index of mean indicator 1. Definition: The relative number calculated by comparing the weighted arithmetic mean of two periods.,Chapter 5 Statistical index,STAT,2. Types of index of mean indicator（平均指标指数） 1) Index of variable construction（可变构成指数，
26、Total change index）,Chapter 5 Statistical index,STAT,Analysis Because of the changes in both average monthly salary and employee structure, the total average salary has dropped 1.72%, means 10 Yuan per person on average.,Chapter 5 Statistical index,STAT,2) Fixed structure index（固定构成指数，Qualitative in
27、dex）,Chapter 5 Statistical index,STAT,Analysis If we rule out the change in the employee structure, then the change of average monthly salary caused the total average salary to rise 9.62%, means 50 Yuan per person on average, and the salary costs the factory 50,000 Yuan more.,Chapter 5 Statistical i
28、ndex,STAT,3) Index of structure influence（结构影响指数，Quantitative index）,Chapter 5 Statistical index,STAT,Analysis If we rule out the change in the average monthly salary, then the change of employee structure caused the total average salary to drop 10.34%, means 60 Yuan less per person on average, and
29、the salary costs the factory 60,000 Yuan less.,Chapter 5 Statistical index,STAT,4) The system of index numbers of mean indicator,Chapter 5 Statistical index,STAT,AnalysisIf we rule out the change in the average monthly salary, then the change of employee structure caused the total average salary to
30、drop 10.34%, means 60 yuan less per person on average.The combined effect of two factor caused the total average salary to drop 1.72%, means 10 yuan less per person on average.,Chapter 5 Statistical index,STAT,Section 5 Multi-factor index number system 1. ConceptTax = SalesTax rate= Sale quantitySal
31、e priceTax rateqmp = q m p 2. Principles 1) Quantitative indicators first, quality indicators second; 2) The production of two neighboring indicators must have real economical meaning; 3) When analyzing the influence of a factor, keep the factors on the back at the base period, while keep the factor
32、s on the front at the report period （前报后基）.,Chapter 5 Statistical index,STAT,Example Tax = Sale quantitySale priceTax rateqmp = q m p,Chapter 5 Statistical index,STAT,Section 6 Some economical index in practice 1. The questions 1) Aggregate index and mean index based on Aggregate index , require tho
33、rough data to make, which is quite difficult in practice.,2) Thoughts on improvement,Chapter 5 Statistical index,STAT,2. Retail Price Index（零售价格指数，P729） 1) Classifying the merchandises and picking the representatives All merchandises：Big class, Medium class, Small class, Group of merchandises Pickin
34、g the representatives。 (1) 14 big classes Food; Beverage, tobacco and alcohol; Clothing; Textiles; Medicine; Cosmetics; Publications; Stationer goods, etc. (2) Food 10 medium class including: Grain; Grease; Meat and eggs; Aquatic products; Fresh vegetable; Dried vegetable; Fresh fruits; Dried fruits
35、; Other food; Restaurant food. (3) Grain 2 small class: refined grain and coarse grain. (4) Refined grain 4 groups of merchandises: Flour, rice, sticky rice, fine dried noodles（挂面）. (5) Flour Standard flour representative（标准粉）.,Chapter 5 Statistical index,STAT,2) Acquiring the price data and calcula
36、ting the average price (1) Investigation points: 35 points in major cities; 12 points in small cities; (2) Calculating the chronological average of the prices. 3) The formulas and the sources of weights.,Chapter 5 Statistical index,STAT,4) Calculation Steps: Index of the representatives Index of Gro
37、ups of merchandises Index of the small classes Medium classes Big classes Total index.,Chapter 5 Statistical index,STAT,(1) Index number of merchandise group,Chapter 5 Statistical index,STAT,(2) Index number of small class (Refined grain),Chapter 5 Statistical index,STAT,Exercise 1. The product of a
38、 factory has increased 5% from the base period to the report period, while cost for every product reduced 5%. So the total cost of the factory remains the same. ( ) Answer: Wrong. 0.25% 2. The data of a market is as following (unit: Yuan). Try to find the influence of sale quantity and sale price on
39、 the change of sales (sales is rounded to integers).,Chapter 5 Statistical index,STAT,2.,Chapter 5 Statistical index,STAT,3. After the prices dropped, the same amount of RMB can buy 15% more products. Whats the price index? 4. If the retail sales of a city in base period is 86 million Yuan. It incre
40、ased to 128.9 million Yuan in the report period. The price index raised 15%. Make a factor analysis based on there numbers. 5. The total cost of a product is 129,000 Yuan in the report period, which is 9000 Yuan more than it costs in the base period. And the cost per unit decreased 3% in the report
41、period. Try to factor analyze the fact.,Chapter 5 Statistical index,STAT,4. If the retail sales of a city in base period is 86 million Yuan. It increased to 128.9 million Yuan in the report period. The price index raised 15%. Make a factor analysis based on there numbers.,Chapter 5 Statistical index
42、,STAT,5. An company has 3 factories producing a same product. What influence do changes of cost per unit and output structure of 3 factories have on the total average cost?,Chapter 5 Statistical index,STAT,5. An company has 3 factories producing a same product. What influence do changes of cost per
43、unit and output structure of 3 factories have on the total average cost?,Chapter 5 Statistical index,STAT,5. An company has 3 factories producing a same product. What influence do changes of cost per unit and output structure of 3 factories have on the total average cost?,Chapter 5 Statistical index
44、,STAT,6. Calculate the total cost index and output index of the following 3 products.,Chapter 5 Statistical index,STAT,7. The total industrial product of region A has increased 17.8% in 2003 than last year; rule out the factor of price rising, the real increscent is 14.6%. So: (1) The “real” incresc
45、ent of 14.6% is caused by what factor? (2) Did the overall price of industrial products raised or dropped in 2003? How much? Solution: (1) The increase of products output. (2) Total industrial product value index Industrial products price index Products output index117.8 Industrial product price index 114.6 So: The industrial products price index 102.79,
