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AHSEC -CLASS 11: ECONOMICS COMPLETE NOTES - PART A

Part A: Statistics for Economics Complete notes (50 Marks expected)
Q.1. What is economics? Who is called father of economics and statistics?
Ans: Economics is the science which studies human behaviour as a relationship between scare means and ends.
Adam smith is called father of economics.
Gottfried Achenwall is called father of statistics.
Q.2. Define the term Statistics. What are its Characteristics? Mention its Functions and Limitations.
Ans: Statistics: The word Statistics seems to have been derived from the Latin word “status” or the Italian word Statista.
By Statistics we mean aggregates of facts affected to a marked extent by multiplicity of causes, numerically expressed, enumerated or estimated according to reasonable standards of accuracy, collected in a systematic manner for a predetermined purpose and placed in relation to each other.
Characteristics of Statistics:
(i) Statistics are aggregates of facts. (ii) Statistics must be numerically expressed.  (iii) Statistics should be capable of comparison and connected to each other. (iv) Statistics should be collected in a systematic manner. (v) Statistics should be collected for a definite purpose.
Importance of Statistics: Statistics is widely used in many fields.

a] Importance to the Government
Ø  Statistics is used in administration and efficient
Ø  functioning of departments. It collects data to fulfill its welfare objectives.
b] Importance of Statistics in Economics:
Ø  Statistics helps in making economic laws like law of demand and concept of elasticity.
Ø  It helps in understanding and solving economic problem.
Ø  It helps in studying market structure.
Ø  It helps in finding mathematical relations between variables.
Limitations of statistics are as follows:
(i) Statistics deals only with quantitative characteristics. (ii) Statistics deals with aggregates not with individuals. (iii) Statistical laws are not perfectly accurate. (iv) Statistical results are only an average.  (v) Statistics is only one of the methods of studying a problem. Statistical tools do not provide the best solution under all circumstances. (vi) Statistics can be misused.
Q.3. What are various types of Statistical Data? Mention their merits and demerits.
Ans: Statistical data are of two types
(a) Primary data
(b) Secondary data.
Primary Data: Data which are collected for the first time for a specific purpose are known as Primary data. For example: Population census, National income collected by government, Textile Bulletin (Monthly), Reserve bank of India Bulletin (Monthly) etc.
Secondary Data: Data which are collected by someone else, used in investigation are knows as Secondary data. Data are primary to the collector, but secondary to the user. For example: Statistical abstract of the Indian Union, Monthly abstract of statistics, Monthly statistical digest, International Labour Bulletin (Monthly).
Merits and Demerits of Primary Data:
Merits:
(a) They are reliable and accurate. (b)  It is more suitable if the field of enquiry is small.
Demerits:
(a) It the field of enquiry is too wide, it is not suitable. (b) Collection of primary data is costly and time consuming. (c) Personal Bias may affect the data.
Merits and Demerits of Secondary Data:
Merits:
(a) While using secondary data, time and labour are saved. (b) It may also be collected from unpublished form.
Demerits:
(a) Degree of accuracy may not be acceptable. (b) Secondary Data may or may not fit the need of the project. (c) Data may be influenced by personal bias.
Q.4. Distinguish between Primary data and Secondary data.
Ans: Difference between Primary Data and Secondary Data:
(a) Primary data are those which are collected for the first time and thus original in character. While Secondary data are those which are already collected by someone else.
(b) Primary data are in the form of raw-material, whereas Secondary data are in the form of finished products.
(c) Data are primary in the hands of institutions collecting it while they are secondary for all others.
Q.5. What are various sources of Secondary Data? Mention the points which should be considered before using secondary data.
Ans: Sources of Secondary Data:
(a) Official publication by the central and state governments, district Boards. (b) Publication by research institutions, Universities etc. (c) Economic Journals. (d) Commercial Journals. (e) Reports of Committees, commissions.
Precautions in the use of Secondary Data:
(i) Suitability: The investigator must check before using secondary data that whether they are suitable for the present purpose or not.
(ii) Adequacy: The investigator has to determine whether they are adequate for the present purpose of investigators.
(iii) Dependability. 
(iv) Units in which data are available.
Q.6. What are various essential qualities of Secondary data? Explain some effective methods of collecting primary data.
Ans: Qualities of Secondary Data:
(a) Data should be reliable (b) Data should be suitable for the purpose of investigator. (c) Data should be adequate (d) Data should be collected by trained investigator.
Methods of collecting primary Data
(a)  Direct Personal Observation: Under this method, the investigator collects the data personally from the persons concerned.
(b) Indirect Oral Investigation: - Under this method, the investigator collects the data from third parties capable of supplying the necessary information.
(c) Schedule and questionnaire: A list of question regarding the enquiry is prepared and printed and send to the person concerned.
(d) Local reports: - This method gives only approximate results at a low cost.
Q.7. What are various stages involved in statistical investigation? Explain them briefly.
Ans: Various stages in statistical investigation: There are five stages in a statistical investigation which are given below:
(i) Collection of Data.
(ii) Organisation of Data: Organising of data involves three steps which are (a) Editing of data (b) Classification of data according to some common characteristics and (c) Tabulation.
(iii) Presentation of Data.
(iv) Analysis: After collection, organisation and presentation, data are analysed.
(v) Interpretation: The last stage is interpretation which is a difficult task and requires a high degree of skill.
Q.8. What is Questionnaire? What are its essential characteristics?
Ans: Questionnaire: A Questionnaire is simply a list of questions in a printed sheet relating to survey which the investigators asks to the informants and the answers of the informants are noted down against the respective questions on the sheet.
Characteristics of an ideal Questionnaire:
(i) The Schedule of question must not be lengthy.
(ii) It should be clear and simple.
(iii) Questions should be arranged in a logical sequence.
(iv) The Units of information should be Cleary shown in the sheet.
Q.9. Define the term population and sample. What is sample and census survey? Distinguish between them.
Ans: Population and Sample
Population: Statistics is taken in relation to a large data. Single and unconnected data is not statistics. In the field of a statistical enquiry there may be persons, items or any other similar units. The aggregate of all such units under consideration is called “Universe or Population”.
Sample: If a part is selected out of the universe then the selected part or portion is known as sample. Sample is only a part of the universe.
Sample survey and Census Survey:
Sample survey: It is a survey under which only a part taken out of the universe is investigated. It is not essential to investigate every individual item of the Universe.
Census survey and complete enumeration: Under Census survey detail information regarding every individual person or item of a given universe is collected.
Difference between Census and Sample survey:
The following are the differences between Census and Sample method of investigation:
(a) Under Census method, each and every individual item is investigated whereas under sample survey only a part of universe is investigated.
(b) There is no chance of sampling error in census survey whereas sampling error cannot be avoided under sample survey.
(c) Census survey is more time consuming and costly as compared to sample survey.
(d) Census survey is an old method and it less systematic than the sample survey.
Q.10. Mention the Merits and Demerits of Census and Sample Survey.
Ans: Merits and Demerits of Census:
Merits:
(a) Since all the individuals of the universe are investigated, highest degree of accuracy is obtained.
(b)  It is more suitable if the field of enquiry is small.
Demerits:
(a) It the field of enquiry is too wide, it is not suitable.
(b) Collection of data is costly and time consuming.
Merits and Demerits of sample survey:
Merits:
(a) Time and labour are saved. (b) It may also be collected from unpublished form. (c) If secondary Data are available, they are much quicker to obtain than primary data.
Demerits:
(a) Degree of accuracy may not be acceptable. (b) Data may or may not fit the need of the project. (c) Data may be influenced by personal bias of investigator.
Q.11. What are various types of diagrams and graphs? Distinguish between diagrams and graphs. What are the uses and limitations of diagrams and graphs?
Ans: Types of diagrams and Graphs:
a) Simple Bar Chart b) Multiple Bar Chart or Cluster Chart c) Staked Bar Chart or Sub-Divided Bar Chart or Component Bar Chart d) Simple Component Bar Chart e) Percentage Component Bar Chart f) Sub-Divided Rectangular Bar Chart g) Pie Chart
Types of Diagrams/Charts:
a) Histogram b) Frequency Curve and Polygon c) Lorenz Curve d) Histogram  

Difference Between Diagrams And Graphs
a)      A graph needs a graph paper but a diagram can be drawn on a plain paper.
b)      As diagrams are attractive to look at, they are used for. Graphs on the other hand are more useful to statisticians and research workers for the purpose of further analysis.
c)       For representing frequency distribution, diagrams are rarely used when compared with graphs. For example, for the time series graphs are more appropriate than diagrams.
Uses of Diagrams and Graphs:
Diagrams and graphs are extremely useful due to the following reasons:
(i) Information presented though diagrams and graphs can be understood easily just in a bird’s eye view.
(ii) Diagrams and graphs produce a greater lasting impression on the mind of the readers.
(iv) They facilitate ready comparison of data over time and space.
However, graphic and diagrammatic presentations have some limitations:
(i)      Unlike a table a diagram or a graph does not show the exact value of a variable.
(ii)    Further, a limited set of facts can be presented through such devices like diagram and graph.
Q.12. What do you mean by index numbers? What are its features?     
Ans:  Index number is an indicator of changes in prices and quantities. It is a specialized average designed to measure the change in a group of related variables over a period of time. It is also an indicator of inflationary or deflationary tendencies. Following are the various feature of index number:
1. Measures of relative changes: - Index number measure relative or percentage changes in the variable over time.
 2. Quantitative expression: - Index numbers offer a precise measurement of the quantitative change in the concerned variable over time.
 3. Average: - Index number show changes in terms of average.
Q.13. Mention few uses of index numbers. Or why index number is called economic barometer? What are its limitations?
Ans: Advantages of index number
1. Measurement of change in the price level or the value of money. 2. Index number helps to ascertain the living standards of people. 3. Price index numbers serve as a useful guide to the business community in planning. 4. Index of exports and imports provides useful information regarding foreign trade.
Limitation of index number
1. Not completely true: - Index number not fully true.  2. International comparison is not possible 3. Limited use: - Index numbers are prepared with certain specific objective.
Q.14. what are the problems in the constructions of index numbers?
Ans:  Following are the main Problems in the construction of index number
1. Purpose of index number. 2. Selection of base year. 3. Selection of goods and services. 4. Selection of price 5. Choice of average (simple or geometric average). 6) Selection of appropriate weights. 7) Selection of appropriate formula (Fisher’s or Laspeyre’s).
Q.15.Define cost of living index number. What are the uses of cost of living index number?
Ans: - Cost of living index number (CLI):- Cost of living index numbers generally represent the average change in prices over a period of time, paid by a consumer for a fixed set of goods and services.
Uses of cost of living index:
1. CLI numbers are used for adjustment of dearness allowance to maintain the same standard of living. 2. It is used in fixing various economic policies. 3. Its helps in measuring purchasing power of money.  4. Real wages can be obtained with the help of CLI numbers.
Q.16. Which is the most ideal formula for constructing index no. and Why?
Ans: - Fisher’s index is regarded as ideal index because:-
i)           It considers both base year and current year’s price and quantity.
ii)          It satisfies both time reversal and factor reversal test.
iii)        It is based on Geometric mean which is theoretically considered to be the best average of constructing index number.
iv)        It is free from bias as it considers both current year and base year price and qty.
Q.17. Define Correlation analysis. What are its various kinds?
Ans: - Definition: - Correlation is the degree of the relationship between two or more variables. It does not explain the cause behind the relationship.
Kinds of correlation may be studied on the basis of:
(a) Linear correlation: - Correlation is said to be linear when one variable move with the other variable in fixed proportion
(b) Non-linear correlation: - Correlation is said to be non-linear when one variable move with the other variable in changing proportion.
(c) Simple correlation: - When only two variables are studied it is a simple correlation.
(d) Partial correlation: - When more than two variables are studied keeping other variables constant, it is called partial correlation.
(e) Multiple correlations: - When at least three variables are studied and their relationships are simultaneously worked out, it is a case of multiple correlations
Q.18.What are the uses and limitations of Correlation?
Ans: - Following are the main advantages of correlation:
1. It gives a precise quantitative value indicating the degree of relationship existing between the two variables.  2. It measures the direction as well as relationship between the two variables.  3. The effect of correlation is to reduce the range of uncertainty in predictions.
Following are the main limitations of correlation:
1. Extreme items affect the value of the coefficient of correlation.  2. Its computational method is difficult as compared to other methods.  3. It assumes the linear relationship between the two variables, whether such relationship exist or not.
Q.19. What are the different degrees of Correlation?
Ans: The different degrees of correlation are:                         
i)     Perfect Correlation: - It two variables vary in same proportion, and then the correlation is said to be perfect correlation.
ii)    Positive Correlation: - If increase (or decrease) in one variable corresponds to an increase (or decrease) in the other, the correlation is said to be positive correlation.
iii)  Negative Correlation: - If increase (or decrease) in one variable corresponds to a decrease (or increase) in the other, the correlation is said to be positive correlation.
iv) Zero or No Correlation: - If change in one variable does not other, than there is no or zero correlation.
Q.20. Explain Karl Pearson’s coefficient of correlation and spearmen’s rank correlation.
Ans: Karl Pearson’s Coefficient of correlation:  The Correlation coefficient (r), also called as the linear correlation coefficient measures the strength and direction of a linear relationship between two variables. The value of r lies between -1 to +1.
Spearman’s rank Coefficient of correlation: - This is a qualitative method of measuring correlation co-efficient. Qualities such as beauty, honesty, ability, etc. cannot be measured in quantitative terms. So, ranks are used to determine the correlation coefficient.
Q.21.What are the desirable properties of a good average and good measure of dispersion.
Ans: - The following are the important properties which a good average should satisfy:
a) It should be easy to understand. b) It should be simple to compute. c) It should be based on all the items. d) It should not be affected by extreme values. e) It should be rigidly defined.  f) It should be capable of further algebraic treatment.
Q.22.Define Arithmetic Mean (A.M). What are its properties? Explain its merits and demerits.
Ans: - Arithmetic Mean: - It is a value obtained by adding together all the items and by dividing the total by the number of items. It is also called average. It is the most popular and widely used measure for representing the entire data by one value. 
Properties of arithmetic mean:
1.       The sum of deviations of the items from the arithmetic mean is always zero i.e.  ∑(X–X) =0.
2.       The Sum of the squared deviations of the items from A.M. is minimum that is less than the sum of the squared deviations of the items from any other values.
Merits of A.M.:
Ø  It is simple to understand and easy to calculate.
Ø  It is affected by the value of every item in the series.
Ø  It is capable of further algebraic treatment.
Demerits of A.M.:
Ø  It is affected by extreme items i.e., very small and very large items.
Ø  It can hardly be located by inspection.
Q.23.Define Geometric Mean (G.M). Mention its merits and demerits. What are its Uses?
Ans:  G.M.:-It is defined as nth root of the product of n items or values. i.e., G.M. = n√ (x1. x2. x3 ……xn)
Merits of G.M.:-
Ø  It is not affected by the extreme items in the series.
Ø  It is rigidly defined and its value is a precise figure.
Ø  It is capable of further algebraic treatment.
Demerits of G.M.:-
Ø  It is difficult to understand and to compute.
Ø  It cannot be computed when one of the values is 0 or negative.
Q.24.Define Harmonic Mean (H.M). Mention its merits and demerits. What are its Uses?
Ans: - H.M.:- It is defined as the reciprocal of the arithmetic mean of the reciprocal of the individual observations.
Merits of H.M.:-
Ø  Like AM and GM, it is also based on all observations.
Ø  It is capable of further algebraic treatment.
Demerits of H.M.:-
Ø  It is difficult to understand and to compute.
Ø  It cannot be computed when one of the values is 0 or negative.
Q.25.Define Median. Mention its merits and demerits.
Ans: Median: Median may be defined as the size (actual or estimated) to that item which falls in the middle of a series arranged either in the ascending order or the descending order of their magnitude. It lies in the centre of a series and divides the series into two equal parts. Median is also known as an average of position.
Merits of Median:-
Ø  It is simple to understand and easy to calculate, particularly is individual and discrete series.
Ø  It is not affected by the extreme items in the series.
Ø  It can be determined graphically.
Demerits of Median:-
Ø  It does not consider all variables because it is a positional average.
Ø  The value of median is affected more by sampling fluctuations
Ø  It is not capable of further algebraic treatment. Like mean, combined median cannot be calculated.
Q.26.Define Mode. Mention its merits and demerits.
Ans: - Mode: - Mode is that value a dataset, which is repeated most often in the database. In other words, mode is the value, which is predominant in the series or is at the position of greatest density. Mode may or may not exist in a series, or if it exists, it may not be unique, or its position may be somewhat uncertain.
Merits of Mode:-
Ø  Mode is the most representative value of distribution, it is useful to calculate model wage.
Ø  It is not affected by the extreme items in the series.
Ø  It can be determined graphically.
Demerits of Mode:-
Ø  It is not based on all observations.
Ø  Mode cannot be calculated when frequency distribution is ill-defined
Ø  It is not capable of further algebraic treatment. Like mean, combined mode cannot be calculated.
Q.27. What is the relationship between mean, median and mode? Give the formula.
Ans: - In a normal distribution Mean = Median = Mode.  In an asymmetrical distribution median is always in the middle but mean and mode will interchange their positions or values. Mode = 3 Median - 2 Mean.
Q.28. What is Dispersion? What are its various types? Distinguish between absolute and relative measures of dispersion.
Ans: - Dispersion: Dispersion is the measure of variation of items. It measures the extent to which the items vary from central value. It is also known as average of the second order. It includes range, mean deviation, quartile deviation, and standard deviation.
Measure of dispersion may be broadly classified into two types:-
A) Absolute measures of dispersion: It is classified into
a) Range b) Mean Deviation c) Standard Deviation d) Quartile Deviation
B) Relative measures of dispersion: It is classified into
a) Coefficient of Range b) Coefficient of Mean Deviation  c) Coefficient of Variation d) Coefficient of Quartile Deviation.
Q.29.Define Standard Deviation (S.D).Mention its merits and demerits.
Ans: - S.D: - The standard deviation, commonly denoted by ‘σ’ (Sigma) is the most widely used measure of dispersion. It is the square root of the second moment of dispersion and is calculated from the arithmetic mean. In short, it may be defined as the root-mean-square deviation from the mean.
Merits of SD:-
Ø  It is based on each and every item of the data and it is rigidly defined.
Ø  It is capable of further algebraic treatment. Combined SD of two or more groups can be calculated.
Ø  It is less affected by fluctuations of sampling than most other measures of dispersion.
Ø  SD is most prominently used in further statistical work.
Demerits of SD:-
Ø  It is not easy to calculate and to understand.
Ø  It gives more weight to extreme items and less to those which are nearer to mean.
Q.30. Difference between Schedule and Questionnaire.
Sl.No
Questionnaire
Schedule
1.
Data collection is cheap and economical.
Data collection is more expensive.
2.
It is not clear that who replies.
Identity of respondent is not known.
3.
No personal contact is possible in case of questionnaire.
Direct personal contact is established
4.
Wider and more representative distribution of sample is possible.
There remains the difficulty in sending enumerators over a relatively wider area.
5.
This is not possible when collecting data through questionnaire.
Along with schedule observation method can also be used.

Q.31. What are various parts of the table?
Ans: In general, a statistical table consists of the following eight parts. They are as follows:
(i) Table Number: Each table must be given a number.
(ii) Title of the Table: Every table should have a suitable title.
(iii) Caption: Caption refers to the headings of the columns.
(iv) Stub: Stub refers to the headings of rows.
(v) Body: It contains a number of cells. Cells are formed due to the intersection of rows and column.
(vi) Head Note: The head-note contains the unit of measurement of data.
(vii) Foot Note: A foot note is given at the bottom of a table.
(viii)Source Note: The source note shows the source of the data presented in the table.
Q.32.What do you mean by Sampling? What are its various types? Mention its features, advantages and disadvantages.
Ans: Meaning of Sampling and Its Types
Sampling refers to the statistical process of selecting and studying the characteristics of a relatively small number of items from a relatively large population of such items, to draw statistically valid inferences about the characteristics about the entire population.
Some of the most common types of random sampling methods are
(1) simple random sampling,
(2) systematic sampling,
(3) stratified sampling, and
(4) cluster sampling.
Simple random sampling ensures that each possible sample has an equal probability of being selected, and each item in the entire population has an equal chance of being included in the sample.
In systematic sampling the items are selected from the population at a uniform interval defined in terms of time, order or space.
In stratified sample the entire population is divided in relatively homogeneous group.
In cluster sampling the population is divided into groups or clusters, a sample of these clusters may be drawn.
Characteristics of the sampling technique (Essentials of a Good sampling)
1. Representative: The sample should truly represent the characteristics of the verse.
2. Adequacy: The size of the sample should be adequate.
 3. Homogeneity: There should be homogeneity in the nature of all the units selected.
4. Independent ability.
Advantages of sampling 
1. Very accurate.
2. Economical in nature.
3. Very reliable.
Disadvantages of sampling
1. Inadequacy of the samples.
2. Chances for bias.                                                                                                         
3. Problems of accuracy.
Q.33. What are various types of Statistical errors?
Ans: Types of Statistical errors: 1] Sampling errors 2] Non-sampling errors
Sampling Error: It is the difference between sample value and actual value of a characteristic of a population.
Non-sampling errors: Errors that accurate the stage of collecting data.

Practical Problems: Consult your teacher
1. One Question from mean, median or mode
2. One Question from MD, SD or variance (Objective)
3. Index number
4. Correlation
5. Preparation of Frequency Distribution table
6. Diagram – Bar diagram
7. Graph – Ogive, histogram and frequency polygon
Q. Calculate Mean, Median, Mode, Q1, Q3, QD, D9 and P60 from the below mentioned data:
a) 4, 4, 3, 3, 4, 5, 7, 8, 7, 8, 15, 20, 10, 3.
b) 1, 2, 3, 4, 5, 6
Q. Find the weighted AM of 1, 2, 3, and 4 with corresponding weights 4, 3, 2, and 1 respectively.
Q. Calculate Mean, Median, Mode, Q1, Q3, QD, D9 and P60 from the following data:
X
10
20
30
40
50
F
5
6
10
5
4
Q. Find Mean, Median, Mode, D5, Q1, Q3, QD and P40
Class :
15 – 25
25 – 35
35 – 45
45 – 55
55 – 65
65 – 75
Frequency :
4
11
19
14
0
2
Q. Find Mean, Median, Mode, D5, Q1 and P40
Marks
Below 10
10 – 20
20 – 30
30 – 40
40 – 50
50 – 60
60 - 70
Above 70
No. of Students :
5
25
40
70
90
40
20
10
Q. Find Range, SD, mean deviation about median, Q1 and Q3 of the following data: Wt (kg): 3, 4, 8, 10, And 12
Q. From the following data, find Range, QD, MD about Mean and Median, standard deviation and CV.
X:
10
11
12
13
14
15
16
Y:
2
7
11
15
10
4
1
Q. Find the mean, QD, S.D., coefficient of SD and coefficient of variation:
Age
20 – 25
25 – 30
30 – 35
35 – 40
40 – 45
45 – 50
50 – 55
55 – 60
No. of Persons
50
70
100
180
150
120
70
60
Q. Calculate Rank correlation from the data given below:
X:
39
62
62
90
82
75
75
98
36
78
Y:
47
53
58
58
62
68
60
91
51
84
Q. Calculate Rank correlation:
Rank 1
2
3
4
5
1
9
7
8
4
Rank 2
1
3
5
2
4
6
9
7
8
Q. Calculate the correlation coefficient by Pearson’s formula of the following data:
X
6
2
10
4
8
Y
9
11
?
8
7
Q. Find the simple aggregative index number and simple average of price relatives (AM) for the data given below:
Commodity
A
B
C
D
E
Base Price
Current Price
40
50
22
25
31
29
10
12
75
100
Q. Find the index number by using (i) Unweighted (ii) Weighted aggregative method (AM Method) from the following data:
Commodities
Base Price (2005)
Current Price (2010)
Weight
Rice
Dal
Fish
Potato
Oil
36
30
130
40
100
54
50
155
35
110
10
3
2
4
5
Q. From the given data calculate the following:
Commodity
1990
1993
Price
Quantity
Price
Quantity
A
B
C
D
6
2
4
10
50
100
60
3
10
2
6
12
56
120
60
24
1. Laspeyre’s Price Index and Laspeyre’s Quantity Index
2. Paasche’s Price index and Paasche’s Quantity index
3. Fisher’s price index and Fisher’s Quantity index
Q. Calculate CLI (Weighted) and unweighted index number:
Expenditure
Food
Rent
Clothes
Petrol
Medicine
Others
% of Exp.
Prices in 1975
Prices in 1976
35%
50
40
10%
40
40
20%
30
40
15%
30
35
15%
10
20
5%
10
15
Q. Construct the general index number from the following data:

Group
A
B
C
D
E
Group Index
Weight
152
48
110
5
130
10
100
12
80
15

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