(a) Originality: Project must not be copied but an original work of investigator.
(b) Sample Selection: Sample must be randomly selected. There must not be any bias in selection of the sample else the entire motto of preparing project will defeat.
(c) Decision Making: Many decisions are required to be taken in making of a project. Therefore, decision making is another important value.
(d) Communication Skills: In order to get information from people, one needs to be tactful. It calls for good communication skills.

For Wheat
Range = L - S = 25 - 9 = 16
\(Q.D={Q_3-Q_2\over2}\)
First we need to arrange this data in ascending or descending order.

\(Q_1={N+1\over4}th \ item\)
\(={10+1\over4}th \ item\)
=2.75th item
Since 2 and 3 item are equal therefore,
Q₁ =10
\(Q_3={3(N+1)\over4}th \ item\)
= 7.25th item
= 18 + (19 - 18) x 0.75 = 18.75
Q.D=\({18.75-10\over 2}=4.375\)
M.D. about Mean

Mean=\({\sum X\over N}={155\over10}=15.5\)
\(M.D.={\sum |D|\over N}\)
M.D. = 43/10 = 4.3
Mean Deviation about Median
\(Median ={N+1\over 2}th \ item\)
\(={10+1\over 2}th \ item\)
= 5.5^th item
Median = 15.5
Since Mean and Median are equal therefore, M.D. from mean and median will also be equal.
\(S.D=\sqrt{\sum D^2\over N}=\sqrt{35435\over10}\)
= 5.43 snesh
 Coefficient of Variation
=\({S.D\over Mean}\times 100\)
\(={5.43\over 15.5}\times 100=29.45\%\)
For Rice
Range = L - S = 34 - 12 = 22
\(Q.D={Q_3-Q_2\over2}\)
First we need to arrange this data in ascending or descending order.

\(Q_1={N+1\over4}th \ item\)
\(={10+1\over4}th \ item\)
=2.75th item
Since 2 and 3 item are equal therefore ,
Q₁ =12
\(Q_3={3(N+1)\over4}th \ item\)
= 7.25th item
= 22 + (23 - 22) x 0.75
= 22.75
\(Q.D.={22.75-12\over2}\)
\(={10.75\over2}=5.375\)
M.D. about Mean

\(Mean={\sum X\over N}={195\over 10}=19.5\)
\(M.D={\sum |D|\over N}\)
M.D. = 60/10 = 6
Mean Deviation about Median
\(Median={N+1\over2}th \ item\)
\(={10+1\over2}th \ item\)
= 5.5^th item
Since 5^th and 6^th item are equal, 5.5th item
= 18. Median is 18.

\(M.D={\sum |D|\over N}\)
M.D. = 57/10 = 5.7
\(S.D=\sqrt{\sum D^2\over N}\)
\(=\sqrt{512.5\over10}=7.16\)
Coefficient of Variation
\(={S.D\over Mean}\times 100\)
\(={7.16\over19.5}\times 100=36.72\%\)

The term weight refers to the relative importance of the different items in the construction of the index. Generally various items say wheat, rice, kerosene, clothing etc. included in the index are not of equal importance, proper weights should be attached to them to take into their relative importance. Thus there are two types of indices.
1. Unweighted indices-in which no specific weights are attached to various commodities.
2. Weighted indices-in which appropriate weights are assigned to various commodities. The Unweighted indices can be interpreted as weighted indices by assuming the corresponding weight for each commodity being unity. But actually the commodities included in the index are all not of equal importance. Therefore it is necessary to adopt some suitable method of weighting, so that arbitrary and haphazard weights may not affect the results.
There are two methods of assigning weights.
(i) Implicit weighting
(ii) Explicit weighting In implicit weighting, a commodity or its variety is included in the index a number of times. For example if wheat is to be given in an index twice as much times as rice then the-weight of wheat is two whereas in explicit weighting two types of weights can be assigned. i.e. quantity weights or value weights. A quantity weight symbolized by q means the amount of commodity produced, distributed or consumed in some time period. A value weight in the other hand combines price with quantity produced, distributed or consumed and is denoted by v = PQ. For example quantity weights are used in the method of weighted aggregative like Lasperey's, Paasche's index numbers and value weights are used in the method of weighted average of price relatives.

Merits:
(a) Attractive and Impressive: Graphs are attractive and impressive.
(b) Simple and easily understandable: Graphs are easy and simple to understand. Knowledge of mathematics is not required to understand graphs.
(c) Useful in Comparison: Graphs prove very useful in comparing data from one year to another or otherwise.
(d) Helps to understand trend: Graphs help us to understand trend in a variable.
(e) Helps to measure statistical averages: Graphs are used to measure some statistical tools like median, mode, quartiles and correlation etc.
(f) Helps to understand shape of the distribution: We can use graphical presentation to understand if a curve is normal or skewed; if it is upward sloping or downward sloping etc.
(g) Helps in forecasting: It helps us to predict future values on the basis of past statistics.
(h) Graphs are useful in all fields: From sports to education to medical and engineering, in all fields we make use of graphs. They are specifically useful for policy formulation and decision making.
Disadvantages of Graphic Presentation
(a) Time Consuming: Graph making is a time consuming task.
(b) Layman Can't Understand: A layman cannot understand and interpret the data represented graphically.
(c) Not suitable for all types of data: Graphs are not suitable for all types of data.

Statistics plays a very important role in the field of Economics. It is very important tool in the hands of economists. Statistics helps in Economics in many ways. Probably this is why it is a part of Economics syllabus and not any other discipline. Statistics has emerged as a lifeline of Economics. It helps an economist in following ways:
(a) It helps to Understand Economic Problems with a Quantitative Expression: No economy can solve the problem of poverty, population or unemployment without knowing their magnitude and causes. We get to know the magnitude of these problems in our economy on the basis of statistical data. Once we know the magnitude of these problems, we can think of their solutions which are called policies.
(b) Helps in Policy formulation: Policy formulation is not possible without having statical details with us. When our finance minister needs to take a decision on fund allocation to different sectors, he needs statistics; when he announces a poverty alleviation programme, he needs statistics, when he thinks of an employment policy, he needs statistics.
(c) Helps in Forecasting: In Economics, we need to forecast demand, supply, prices etc. we make use of historical data and trend analysis to make such forecasts. It is simply not possible to forecast logically without having statistical details.
(d) Helps in Formulation of theories: An Economic theory is established by developing relationship between economic variables using statistical tools. For example, Statisticians collected data on price and quantity demanded. Statisticians studied this data and found strong negative correlation between price and quantity demanded. So, law of demand was formulated. No theory or law in economics can be developed without help of statistical tools.
(e) Inter-sectoral and Inter-temporal Comparison: Statistics helps us to make inter-sectoral and intertemporal comparison. For example, to understand the problem of poverty, we wish to know the rural and urban poverty scenario. We also want to know state wise dimensions of poverty and we also compare poverty in India with other countries of the world. Similarly, we compare price rise in 2012-13 with price rise in other years. Statistics prove to be of great help in these comparisons.
(f) Developing Cause-Effect Relationship: Statistics help us to develop cause and effect relationship amongst different variables. It helps us to diagnose an economic problem. Once an economic problem is diagnosed, it can be rectified easily. What a diagnostic lab is for a doctor, so is statistics for economics.

The three central problems of an economyare:
(i) What to produce?
(a) What to produce refers to a problem in which decision regarding which goods and services should be produced is to be taken.
(b) Since its resources are limited, every economy has to decide what commodities are to be produced and in what quantities.
(c) The guiding principle for an economy here is to allocate resources in such a way that gives maximum aggregate utility to the society.
(ii) How to produce?
(a) How to produce refers to a problem in which decision regarding which technique of production should be used is made.
(b) Goods and services can be produced in two ways: by using labour intensive techniques, and by using capital-intensive techniques
(c) The guiding principle for an economy in such a case has to decide about the techniques of production on the basis of cost of production. Those techniques of production should be used which lead to the least possible cost per unit of commodity or service.
(iii) For whom to produce? 
(a) For whom to produce refers to a problem in which decision regarding which category of people are going to consume a good, i.e., economically poor or rich.
(b) As we know, goods and services are produced for those who can purchase them or have the capacity to buy them.
(c) Capacity to buy depends upon how income is distributed among the factors of production. The higher the income, the higher will be the capacity to buy and vice versa. So, this is a problem of distribution.
(d) The guiding principle is that the economy must see here that important and urgent wants of its citizens are being satisfied for the maximum possible extent or not.

As, we know condition for consumer equilibrium is, Necessary Condition Marginal utility of last rupee spent on each commodity is same. Suppose there are two commodities, X and Y respectively. So, for commodity X, the condition is, Marginal Utility in terms of Money = Price of X
Or \(\frac { Marginal\ utility\ of\ s\ product\ in\ util[M{ U }_{ x }] }{ Marginal\ utility\ of\ one\ rupee[M{ U }_{ m }] } \)=Price of X
Or \(\frac { M{ U }_{ x } }{ { P }_{ x } } =M{ U }_{ M }\)    ---------(1)
Similarly: for commodity Y, the condition is,
\(\frac { M{ U }_{ y } }{ { P }_{ y } } =M{ U }_{ M }\)  -----------(2)
Putting equation (2) in (1), we get
\(\frac { M{ U }_{ x } }{ { P }_{ x } } =\frac { M{ U }_{ y } }{ { P }_{ y } } \)
But as given in the question that the ratio of marginal utility to price in case of X is higher than that in case of Y,
i.e.,\(\frac { M{ U }_{ x } }{ { P }_{ x } } >\frac { M{ U }_{ y } }{ { P }_{ y } } \)
It means marginal utility from the last rupee spent on commodity X is more than marginal utility from the last rupee spent on commodity Y. So, to attain the equilibrium consumer must increase .the quantity of X, which decreases the MUx and decreases the quantity of Y, which will increase the MU. Increase in quantity of y X and decrease in quantity of Y continue till \(\frac { M{ U }_{ x } }{ { P }_{ x } } =\frac { M{ U }_{ y } }{ { P }_{ y } } \)

Calculation of Arithmetic mean by direct method

\(\overline { x } =A+\frac { \sum _{ i=1 }^{ n }{ { f }_{ i } } { m }_{ i } }{ \sum _{ i=1 }^{ n }{ { f }_{ i } } } \quad \quad \quad \)
26 (40+M)=1060+50M
1040+26M=1060+25M
26M-25M=1060-1040
M=20

\(M=\frac{\frac{N}{2}-cf}{f}\times c;M=\frac{47.5-38}{12}\times10\)
\(M=30+\frac{95}{12}\) 
M = 30 + 7.91
Median = 37.91

(i) Selling cost is the expenses which are incurred for promoting sales or inducing customers to buy a good of a particular brand.
(ii) Theoretically, a consumer is the king because whatever he desires/ demands is produced/ supplied.
(iii) But in reality this is not so. Advertisement and salesmanship bias his mind in favour of certain commodities which otherwise may not be good.

Different types of two-dimensional diagrams have been explained below: Rectangles: Since area of a rectangle is equal to the product of its length and width, while making such type of diagrams both length and width are considered. Rectangles are suitable for use in cases where two or more quantities are to be compared and each quantity is sub-divided into several components. Squares: To construct a square diagram, first the square-root of the values of various figures to be represented is taken and then these values are divided either by the lowest figure or by some other common figure to obtain proportions of the sides of the squares. The squares constructed on these proportionate lengths must have either the base or the center on a straight line. The scale is attached with the diagram to show the variable value represented by one square unit area of the squares. Circles: Circles are alternatives to squares to represent data graphically. The circles are also drawn such that their areas are in proportion to the figures represented by them. The circles are constructed in such a way that their centers lie on the same horizontal line and the distance between the circles is equal. Since the area of a circle is directly proportional to the square of its radius, the radii of the circles are obtained in proportion to the square root of the figures under representation. Thus, the lengths that were used as the sides of the square can also be used as the radii of circles.

(i) MR is calculated in the reverse order, i.e., from bottom to top.
(ii) MR of the 4th unit has not been calculated as the total revenue from 3 units is not given.