If at a given price there is excess supply as shown in the given figure.

In the given figure, the excess supply of AB at price P₁ will create a competition among the producers, which will reduce the price from P₁ to P. It can be explained in the following cases:
(i) Downward movement along the supply curve (Contraction in supply): Due to excess supply of AB, the competition among the producers will reduce the price. As we know, positive relationship exists between price and quantity supplied. So fall in price P₁ to P leads to fall in supply from B to E.
(ii) Downward movement along the demand curve (Expansion in demand): Due to excess supply of AB, the competition among the producers will reduce the price. As we know inverse. relationship exits between price and quantity demanded. So, fall in price from P₁ to P, leads to rise in demand from A to E. It can be explained with the help of the following schedule

In the above schedule at price 5, there is excess supply. This excess supply, leads to fall in price till we reach the equilibrium at price 3.
Note: Contraction in supply and expansion in demand have to be done simultaneously to reach the equilibrium.

(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.

We need an index number because:
Index numbers are indispensable tools of economics and business analysis.
Following are the main uses of index numbers.
1. Index numbers are used as economic barometers: Index number is a special type of averages which helps to measure the economic fluctuations on price level, money market, economic cycle like inflation, deflation etc.
2. They are useful in forecasting future economic activity: Index numbers are used not only in studying the past and present workings of our economy but also important in forecasting future economic activity. Index numbers measure the purchasing power of money. Index of Exports and Imports provides relevant information regarding foreign trade and accordingly government can formulate its export-import policy, business men who are engaged in foreign trade can take their decisions and one can predict changes in inflow or outflow of foreign exchange.
3. The cost of living index numbers determine whether the real wages are rising or falling or remain constant: The real wages can be obtained by dividing the money wages by the corresponding price index and multiplied by 100. Real wages helps us in determining the purchasing power of money. Index numbers are used in deflating. Index numbers are highly useful in deflating i.e. they are used to adjust the wages for cost of living changes and thus transform nominal wages into real wages, nominal income to real income, nominal sales to real sales etc. through appropriate index numbers.
4. Used in Deflating: Deflating means correcting or adjusting a value which has inflated. It makes allowances for the effect of price changes. When prices rise, the purchasing power of money declines. If the money incomes of people remain constant between two periods and prices of commodities are doubled the purchasing power of money is reduced to half. For example if there is an increase in the price of rice from Rs.10/ kg in the year 1980to Rs.20/kg in the year 1982. then a person can buy only half kilo of rice with no. so the purchasing power of a rupee is only 50paise in 1982 as compared to 1980.
Thus the purchasing power of money \(=\frac { 1 }{ Price\quad Index } \) In times of rising prices the money wages should be deflated by the price index to get the figure of real wages. The real wages alone tells whether a wage earner is in better position or in worst position.
For calculating real wage, the money wages or income is divided by the corresponding price index and multiplied by 100. 
Money wages i.e. Real wages = \(\\ \frac { Money\quad wages }{ Priceindex } \times 100\) 
Thus Real Wage Index \(=\frac { Realwagescurrentyear }{ Realwagesofbaseyear } \times 100\)
5. Index numbers helps in formulating suitable economic policies and planning: Many of the economic and business policies are guided by index numbers. For example while deciding the increase of DA of the employees; the employer's have to depend primarily on the cost of living index. If salaries or wages are not increased according to the cost of living it leads to strikes, lock outs etc. The index numbers provide some guide lines that one can use in making decisions.
6. They are used in studying trends and tendencies: Since index numbers are most widely used for measuring changes over a period of time, the time series so formed enable us to study the general trend of the phenomenon under study. For example for last 8 to 10 years we can say that imports are showing upward tendency. Businessmen need to know the trends in the market to take decisions about wage rates, prices of the product, prices of raw materials etc. Therefore, index numbers are very useful for them.

Following steps are involved in construction of a discrete frequency distribution:
(a) Arrange the series in ascending or descending order: First of all, arrange the raw data in ascending or descending order.
(b) Make as many classes as many are values of variable: Place all values of the variable in the first column of the series beginning with the lowest and giving the highest.
(c) Determine Frequency of each value: To determine frequency of a class, count, how many times a value is repeating itself. For counting, also make a column of tally bars before frequency. A vertical line is put for each repetition and after for five four lines are intersected like this
(d) Place Frequencies:Count the bars. Write it in front of each class in frequency column.
(e) Check Mathematical Accuracy:Total the frequency column to verify if sum total of frequencies is equal to number of total observations. 

Average refers to a measure of central tendency or measure of location. It is a single value which represents the entire set of data. This is a term that is used, mis-used and often over used. Typically, many individuals refer to average when they really mean the arithmetic average (mean). Average can mean the mean, the median and the mode; it can refer to a geometric mean and weighted averages. Characteristics of a Good Average
(i) It should be rigidly defined. If an average is left to the estimation of an observer and if it is not a definite and fixed value it cannot be representative of a series. The bias of the investigator in such cases would considerably affect the value of the average. If the average is rigidly defined; this instability in its value would be no more, and it would always be a definite figure,
(ii) It should be based on all the observations of the series. If some of the items of the series are not taken into account in its Calculation the average cannot be said to be a representative one. As we shall see later on there are some averages which do not take into account all the values of a group and to this extent they are not satisfactory averages.
(iii) It should be capable of further algebraic treatment. If an average dose not possess this quality, its use is bound to be very limited. It will not be possible to calculate, say, the combined average of two or more series from their individual averages; further it will not be possible to study the average relationship of various parts of a variable if it is expressed as the sum of two or more variables. Many other similar studies would not be possible if the average is not capable of further algebraic treatment.
(iv) It should be easy to calculate and simple to follow. If the calculation of the average involves tedious mathematical processes it will not be readily understood and its use will be confined only to a limited number of persons. It can never be a popular average. As such, one of the qualities of a good average is that it should not be too abstract or mathematical and there should be no difficulty in its calculation. Further, the properties of the average should be such that they can be easily understood by persons of ordinary intelligence.
(v) It should not be affected by fluctuations of sampling. If two independent sample studies are made in any particular field, the averages thus obtained, should not materially differ from each other. No doubt, when two separate enquires are made, there is bound to be a difference, in the average values calculated but in some cases this difference would be great while in others comparatively less. These averages in which this difference, which is technically called "fluctuation of sampling" is less, are considered better than those in which its difference is more.

Degree of correlation measures the extent to which items are correlated. Nearer is the value of r to 1 higher is the degree of correlation, nearer is the value of r to zero, closer is the value of r to zero. Direction is indicated by sign of + or -. A + sign indicates positive correlation-i.e. when x increases, y increases and vice verca and a - sign shows negative correlation i.e. when x increases, y decreases and vice versa.

Merits of Standard Deviation:
Among all measures of dispersion Standard Deviation is considered superior because it possesses almost all the requisite characteristics of a good measure of dispersion. It has the following merits:
(a) This is the most rigidly defined measure of dispersion and therefore is dependable.
(b) It is further capable of Algebraic Treatment; Coefficient of S.D., Variance and Coefficient of Variation are used to test the variability and consistency by using S.D.
(c) Unlike Mean Deviation, Combined S.D. for given two or more series can be computed if Xs and S.D. are given.
(d) It is based on all the terms or observations hence is more reliable.
(e) As sum of squares of deviations from X is minimum, so it is the best measure.
(f) Standard Error of the different methods are also based on S.D.
(g) To Compare Variability or Consistency co-efficient of S.D., C.V. is most dependable as compared to Coefficient of Mean Deviation or Q.D. (h) As it is based on A.M.; It has vast good . qualities of A.M.
(i) We can also find sum of terms as well as sum of squares of terms if X and S.D. are given.
Demerits or Limitations
(a) As compared with other measures of dispersion it is more difficult to compute and not so easy to understand.
(b) In the case of open end intervals we have to make the assumption of lower limit of first interval and upper limit of last interval.
(c) As far as S.D. is concerned it does not compare two series itself. We have to proceed to Coefficient of S.D. or c.v. for this purpose.
(d) The extreme terms make the impact two much, therefore in some cases Coefficient of Q.D. or of M.D. has a certain edge over it. If extreme item differ largely, then they make a heavy change when deviations are squared.
(e) It cannot be exactly calculated for a distribution with open-ended classes

difference between graphs and diagrams is as follows:
(a) In the construction of a graph generally graph paper is used which helps us to study the mathematical relationship between two variables. Diagrams are constructed on a plain paper and are used for comparison only and not for studying.
(b) Diagrams furnish only approximate information. It is not useful for further mathematical and statistical analysis.
(c) Diagrams are useful in depicting categorical and geographical data but they fail to present data realting to time series and frequency distribution

After the collection of data, the next step is to present them in some suitable form-statistical table is one of them. Tabulation enables the numerical facts to be presented in such a way that their analysis, interpretation and subsequent computation become easier. Decisionmakers neither have the opportunity nor have enough time to go through bulky data. They want the information in a precise form so that conclusions can be want the information in a precise form so that conclusions can be drawn from them without much wastage of time and energy. Tabulation is thought to be useful tool in this respect. The condensed facts presented in table can be easily visualized and the needed information can be easily sorted out. The comparability of the data increases significantly when they are placed side by side in a table. This also helps the establishment of relationship between different phenomena. Tabulation paves the way for further condensation of the data by presenting them in suitable forms for mathematical treatment. Statistics is the study of large numbers. The study of a large number of cases is difficult unless some process of condensing the information is available The principal objectives of tabulation are stated below:
1. To make complex data simple:
When data are arranged systematically in a table, such data become more meaningful and can be easily understood.
2. To facilitate comparison:
When different data sets are presented in tables it becomes possible to compare them.
3. To economize space:
A statistical table furnishes maximum information relating to the study in minimum space. Statistical tables conserve space and reduce explanatory and descriptive statements to a minimum.
4. To make data fit for analysis and interpretation:
Tabulation serves as a link between the collection of data on the one hand and analysis of such data on the other. In other words, after tabulating the data, it becomes possible to find out their averages, dispersion, and correlation. Such statistical measures are necessary for their interpretation.
5. To provide reference:
A statistical table can be used as a source of reference for other studies of similar nature.
6. Memorizing effect:
The visualization of relations and process of comparison are greatly facilitated by tables. Tabulated data can be more easily remembered than data that are not tabulated.
7. Facilitates Detection of errors:
A tabular arrangement facilitates the summation of items and the detection of errors and omissions and Statistical tables provide a basis for computations.
No, not all tables fulfil these objectives. Only tables drawn keeping essentials of a good table fulfil these objectives.

The following general guidelines are taken into consideration while preparing diagrams:
1. Title: Each diagram should have a suitable title. It may be given either at the top of the diagram or below it. The title must convey the main theme which the diagram intends to portray.
2. Size: The size and portion of each component of a diagram should be such that all the relevant characteristics of- the data are properly displayed and can be easily understood.
3. Proportion of length and breadth: An appropriate proportion between the length and breadth of the diagram should be maintained. As such there are no fixed rules about the ratio of length to width.
4. Proper scale: There are again no fixed rules for selection of scale. The diagram should neither be too small nor too large. The scale for the diagram should be decided after taking into consideration the magnitude of data and the size of the paper on which it is to be drawn. The scale showing the values as far as possible should be in even numbers or in multiples of 5, 10, 20, and so on. The scale should specify the size of the unit and the nature of data it represents, for example, 'millions of tonnes', in ~ thousand, and the like. The scale adopted should be indicated on both vertical and horizontal axes if different scales are used. Otherwise, it can be indicated at some suitable place on the graph paper.
5. Footnotes and source note: To clarify or elucidate any points which need further explanation but cannot be shown in the graph, footnotes are given at the bottom of the diagrams.
6. Index: A brief index explaining the different types of lines, shades, designs, or colours used in the construction of the diagram should be given to understand its contents.
7. Simplicity: Diagrams should be prepared in such a way that they can be understood easily. To keep it simple, too much information should not be loaded in a single diagram as it may create confusion. Thus if the data are large, then it is advisable to prepare more than one diagram, each depicting some identified characteristic of the same data.

When there is no fixed price and price falls with the rise in output, MR curve slope downwards. Producer aims to produce that level of output. at which MC is equal to MRand MC curve cuts the MR curve from below. Let us understand this with the help of following table:

According to Table, both the conditions of equilibrium are satisfied at 4 units of output. MC is equal to MR and MC is rising. MC is more than MR when output is produced after 4 units of output. So, Producer's Equilibrium will be achieved at 4 units of output. Letus understand the determination of equilibrium with the help of a diagram:

Producer's Equilibrium is determined at OQ level of output corresponding to point E as at this point, MC= MR and MC curve cuts MR curve from below.
In Figure, output is shown on the horizontal axis and revenue and costs on the vertical axis. Producer's equilibrium will be determined at OQ level of output corresponding to point E because at this, the following two conditions are met:
(i) MC = MR; and
(ii) MCcurve cuts the MR curve from below.
When MR > MC, then producer will continue to produce as long as MR becomes equal to MC. It is so because firm will find it profitable to raise the output level.
When MR< MC, then producer will cut down the production as long as MR becomes equal to MC. It is so because firm will find it unprofitable to produce an extra unit. So, it starts reducing the level of output till MR= MC.
So, the producer is at equilibrium at OQ units of output.

Primary data refers to the data collected by investigator himself.
Methods of Collection of Primary Data: The primary data are collected by the following methods.
1. Direct personal investigation.
2. Indirect personal investigation
3. Information through correspondents
4. Telephonic Interviews
5. Mailed Questionnaire Method
6. Questionnaire filled by Enumerators
Information from Correspondents According to this method the collection of data is neither through the questionnaire nor through the enumerators but through local correspondents. This method of collecting the data is not reliable and it should be used only at those places where the purpose the investigation is served by rough estimates.
Advantages:
(a) It is very cheap and quick method of collecting data.
(b) This method provides information on regular basis from distant places.
(c) This method involves less labor and time.
Disadvantages:
(a) In this method, correspondent may use any method of collecting data which investigator is relying on.
(b) This method is not so reliable and accurate.
(c) Data may be biased.
(d) It lacks uniformity.
Suitability:
 This method is suitable when scope of enquiry is large and information is required on regular basis.

(i) Revenue Schedules

Cost Schedules

(ii) For quantity of 6 units MRis equal to MC.
(iii) Equilibrium quantity of output occurs where MR = MC.
Equilibrium quantity = 6 units
Equilibrium price = Rs.19
(iv) TR = 114
TC = 109
Total profit = TR- TC = 114 - 109 = 5

According to Horace Secrist, "By Statistics we mean aggregate of facts affected to a marked extent by multiplicity of causes numerically expressed, enumerated or estimated according to a reasonable standard of accuracy, collected in a systematic manner for a pre-determined purpose and placed in relation to each other."
(a) Statistics is aggregate of facts: A single figure is not called statistics. Aggregate of facts is called statistics. 1t is for a simple reason that a single figure can neither be compared, nor presented nor analyzed. If Ram says that his height is 6 feet, it is not statistics but if he says average height of his class is 6 feet, it is a statistical statement because it is backed by aggregate of facts.
(b) Statistics are affected to a marked extent by multiplicity of causes: There are many factors which work behind statistical forces operating together. For example, statistics of employment in an economy are affected by demand and supply of labour force, working conditions, production methods used etc. In the above example, if average height of a class is 6 feet, there are many factors responsible for it- geographical, genetic, gender etc.
(c) Statistics are numerically expressed: All Statistics are numerically expressed. If a fact is not numerically expressed, it cannot be called statistics. Statements like good, bad, very large, very small, inadequate etc. cannot be called statistics. For example, following statements are not statistics. My height has increased; India's population has increased; Crime rate is increasing in India etc. Following are statistical statements. My height which had increased by 2 inches last year has increased by 5 inches this year. India's population is increasing @ 2% p.a. which is more than last year which was 1.2%p.a. Crime rate in India has increased by 200% during 1999-2010.
(d) Statistics are enumerated or estimated according to a reasonable standard of accuracy: Statistical data must be reasonably accurate because they serve as the basis of decision making and conclusions drawn. If data are actually collected they need to be accurate if they are estimated (when actual data are not available) they must be accurate to a reasonable standard.
(e) Statistics are collected in a systematic manner: Only systematically collected statistics are reliable. Those statistics which are not systematically collected are inaccurate and unreliable. Such statistics, if used, will lead to misleading conclusfons.
(f) Statistics are collected for a predetermined purpose: Statistics are collected for a pre-determined purpose. Purpose cannot be determined after collection of data. Which sources should be used for collecting data, which method to use, what should be the sample size all depends on purpose of statistics. If it is not collected for a predetermined purpose, it will be purposeless i.e. useless.
(g) Statistics should be placed in relation to each other: Since statistics are collected for comparison, we need to place various items in relation to each other. Data must be uniform and homogeneous to be able to put in relation to each other. For example, if we are comparing price indices, base year should be same. If it is not so, they are not comparable. Therefore, we can say that all numerical facts are not statistics but all statistics are numerical facts.

Large number of sellers-
(i) The words 'large number' simply states that the number of sellers is large enough to render a single seller's share in total market supply of the product insignificant.
(ii) Insignificant share means that if only one individual firm reduces or raises its own supply, the prevailing market price remains unaffected.
(iii) The prevailing market price is the one which was set through the intersection of market demand and market supply forces, for which all the sellers and all the buyers together are responsible.
(iv) One single seller has no option but to sell what it produces at this market determined price. This position of an individual firm in the total market is referred to as price taker. This is a unique feature of a perfectly competitive market.
Large number of buyers-
(i) The words 'large number' simply states that the number of buyers is large enough, that an individual buyer's share in total market demand is insignificant, the buyers cannot influence the market price on his own by changing his demand.
(ii) This makes a single buyer also a price taker.
To sum up, the feature "large number" indicates ineffectiveness of a single seller or a single buyer in influencing the prevailing market price on its own, rendering him simply a price taker.

Rule: When with the fall in price of goods, total revenue rises, ED > 1, if it remains same ED = 1 and if falls then ED < 1.

The behaviour of Marginal product in the law of variable proportion is as under:
(i) When Marginal product rises (till Point P₁), Total product increases at an increasing rate (convex shape) (till point P).
(ii) When Marginal product falls and remains positive (till point B₁), total product increases at a diminishing rate (concave shape) (till point A).
(iii) When Marginal Product is zero (at point B₁), Total Product is at its maximum and constant (At point B).
(iv) When Marginal product becomes negative (after point B₁), total product falls (after point B).

Causes or Reasons of this Behaviour is as Under:
(i) Phase I
(a) Proper utilization of the fixed factor
1. In the initial stage of production the units of variable input (i.e., labour) is so less that fixed inputs cannot be effectively utilized.
2. Proper utilization of the fixed factor can be attained when more and more units of variable factor (labour units) are applied to the fixed factor (land), the fixed factor will be used intensively and output will increase rapidly.
(b) Specialization and division of labour
1. Initially, there was only one labour working on all the 5 acres of land ploughing, watering, etc.
2. As the number of labour units increases, each worker specialized in a particular activity leads to
specialization of the variable units and this resulted in increased output.
(ii) Phase II
(a) The non-optimal combination of variable factor with the fixed factor
1. When a given quantity of a fixed factor is combined with more and more units of variable factor, the additional units of variable factor will have smaller and smaller quantity of fixed factor to work with them.
2. As many workers share the same fixed factor, the share of each would obviously fall. Therefore, the cooperation of the fixed factor is not available to the same extent. Thus, an increase in the variable factor would add less and less to total output.
(b) Imperfect Substitutes
1. Diminishing return to factor occurs because variable factor and fixed factor are imperfect substitutes to each other.
2. Technically speaking, there is a limit to which variable factor can be applied to fixed factor and that limit depends upon the efficiency of fixed factor. So, variable factor and fixed factor are imperfect substitutes to each other.
(iii) Phase III
(a) Efficiency of Variable Factor Fall
1. In this stage the amount of variable factor becomes excessive relative to the fixed factor. This happens when too many LABOUR are engaged in cultivating on a given piece of land.
2. Instead of helping each other in production they cause overcrowding and chaos and thus hamper each other's work. In such a case, the contribution of additional labour to production is bound to be negative.
3. Thus, the marginal returns become negative and the total returns start diminishing.
(b) Efficiency of Fixed Factor Fall
1. Too much of a variable factors may also lead to the inefficiency of the fixed factor as well. • In case of capital, which is a fixed factor, too much of labour may cause lot of wear and tear of machinery, frequent breakdowns and excessive cost of maintenance. This is bound to affect total production adversely.
2. In such a situation it is advisable to reduce the units of the variable factor than to increase it with a view for getting maximum production.

(i) A rise in price of Substitute good
(a) Increase in Price of Substitute Goods An increase in price of substitute goods (Coke)leads to an increase in demand of a given commodity (Pepsi).The Demand curve of Pepsi would shift rightward It can be explained with the help of given diagram:
In the given diagram the demand curve for Pepsi when the price of Coke is  18 lies to the right of that when the price of Coke is Rs.15. Hence, an increase in the price of a substitute good shifts the demand curve for a product to the right.

(ii) Arise in price of Complimentary good
Increase in Price of Complimentary Good [Refill] leads to a decrease in demand of given commodity [Pen]. The Demand curve for Pen shifts leftwards. It can be explained with the help of given diagram:

In the above diagram, the demand curve for Pen when Refill price is Rs.5 lies to the left of that when the Refill price is Rs.3

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.

Statistical project is an extremely powerful teaching tool that integrates numerous concepts and skills presented in the classroom. Here are some basic guidelines for developing a statistical project.
A statistical project is the process of answering a research question using statistical techniques and presenting the work in a written report. The research question may arise from any field of scientific endeavor, such as athletics, advertising, aerodynamics, or nutrition. A project differs from a statistical poster in that a written report is used to present the findings.
The process of developing a statistical project should demonstrate the scientific method and pose a focused question or questions, collect appropriate data, analyze the data thoughtfully, and draw correct conclusions.
Because students are asking questions continually about what touches their lives, they should have little trouble generating questions about themselves or their schools, families, neighborhoods, or interesting phenomena in the world. Once a question is proposed, students should examine it. First, is it a question that can be answered? Second, can students collect data to answer the question or has someone else already collected data that could be used to find the answer? Once the question is chosen, data must be collected. If published data are used, students should understand how the data were obtained and record their source. Usually, students choose to collect their own data. Time should be spent deciding how to collect this data. If a survey is used, how are the people chosen to answer the questionnaire? Thoughtful analysis of the data may take many forms and should be guided by the question and how the data were collected. Usually, it is best to begin by graphing the data. Can graphs be used to give the answer to the question or questions? Most of the time, graphics have been the sole method of data analysis for grades 4-6. As students gain experience, simple statistical methods such as a chi-squared test or a t-test may be used. Regression has been used occasionally. Sometimes, estimation is most appropriate and hypothesis testing is not needed. Other methods may be used, depending on the question and data.
Once analysis is complete, the question should be answered. The data may not be able to provide a conclusive answer. Finally, consider the strengths and weaknesses of the project. What would be changed if the project was done again?

Index numbers are used as economic barometers. Index number is a special type of averages which helps to measure the economic fluctuations on price level, money market, economic cycle like inflation, deflation etc. G.Simpson and F.Kafka say that index numbers are today one of the most widely used statistical devices. They are used to take the pulse of economy and they are used as indicators of inflation or deflation tendencies. So index numbers are called economic barometers.

Spatial Classification: In spatial classification, data are classified according to geographical areas.
Example: Statewise classification of production of food grains in India:

Chronological classification:
In this type of classification the data are classified according to different time periods.
Example: Population of India for different time periods.
Profits of a business establishment over different years.

As distinct from the arithmetic mean which is calculated from each and every item in the series, the median is what is called 'positional average'. The term position refers to the place of value in a series. The place of the median in a series is such that an equal number of items lie on either side of it, i.e. it splits the observations into two halves.

The given statement is correct. Both the blades of a pair of scissors are equally important to cut a piece of cloth. Similarly, both demand and supply are needed for determining price in the market. There is no use for demand for a product if there is no supply for the product and supply is not needed if there is no demand for the product. One of the two may play more active role in price determination in the short run. But, both are needed to determine the price in the long run.

\(\overline { x } =A+\frac { \sum _{ i=1 }^{ n }{ { f }_{ i } } { m }_{ i } }{ \sum _{ i=1 }^{ n }{ { f }_{ i } } } \)
Let L₁=lower limit
L₂=upper limit
then mid value m=(L₁+L₂)/2

\(\overline { x } =A+\frac { \sum _{ i=1 }^{ n }{ { f }_{ i } } { m }_{ i } }{ \sum _{ i=1 }^{ n }{ { f }_{ i } } } \)=1135/30=37.83
Thus average pocket expenses are Rs. 37.83

Q₁=\(\frac{n}{4}\)observation \(\frac{95}{4}\)=23.75th observation
Q₁ class is 20-30
Q₁=l₁+\(\frac { \left( N/4-C \right) }{ f } \)(i)
Where l₁ = 20; f = 18;\(\frac{N}{4}\)=23.75; C = 20; i = 10
Q₁=20+\(\frac { \left( 23.75-20 \right) }{ 18 } \)(10)=22.08
Q₃ =\(\frac{3(n)}{4}\)th observation \(\frac{3(95)}{4}\)=71.25 observation
Q₃ class is 50-60
Then Quartile of a continuous series can be calculated by the below interpolation formula.
Q₃ = 20 +\(\frac { \left( 3N/4-C \right) }{ f } \)(i)
Where l₁ = 50; f = 15;\(\frac{3N}{4}\)= 71.25; C = 70; i= 10
Q₃ = 50 +\(\frac { \left( 71.25-70 \right) }{ 15 } \)(i)=50.83
Quartile Deviation (Q.D) =\(\frac { { Q }_{ 3 }-{ Q }_{ 1 } }{ 2 } =\frac { 46.42-25 }{ 2 } =\frac { 20.42 }{ 2 } \)
Coefficient of Quartile Deviation = \(\frac { { Q }_{ 3 }-{ Q }_{ 1 } }{ { Q }_{ 3 }+{ Q }_{ 1 } } =\frac { 46.42-25 }{ 46.42+25 } =\frac { 20.42 }{ 71.72 } \)=0.36

The sign of covariance between X and Y determines the sign of the correlation coefficient. The standard deviations are always positive. When covariance is zero, correlation is also zero. Correlation is preferred to covariance as a measure of association because:
(a) It tells about positive, negative, or zero correlation i.e. no linear correlation.
(b) As well as, r is independent of change of origin and change of scale of measurements.

Tabulation is the process of condensing classified data in the form of a table so that it may be more easily understood, and so that any comparison involved may be more readily made. - D. Gregory and H. Ward
It is a medium of communication of great economy and effectiveness for which ordinary prose is inadequate. In addition to its formation in simple presentation, the statistical table is also a useful tool of analysis. -D. W. Paden and E. F. Lindquist
In classification, data are separated and grouped based on a property of the data common to all values.
• In tabulation, data is arranged into columns and rows based on characteristics/properties, or indicators.
• Tabulation often emphasize on the presentation aspects of the data, while classification is used as a means of sorting of data for further analysis.

Sometimes we have such a series in which all values except one are approximate to each other. One value is exceptionally high. In order to provide proper shape, the larger bar is broken at the top and the value of each bar is written on the top. Its purpose is to:
(a) save time
(b) Save space and
(c) To give a proper shape to the diagram

Histogram Graph

The producer will be in equilibrium when MR= MC. It occurs at 4 units of output where both MR and MC are equal to 7

(i) Interdependence means that actions of one firm affects the actions of other firms.
(ii) Since the number of sellers is small, each firm has to take into consideration the possible reaction of its competitors, when making decisions.
(iii) The business decision of a single seller will have a substantial impact on the product price, output and profits of the rival firms.
(iv) For example the "Na tiona1 Newspapers" market, when the "Economic Times" introduced invitation pricing policy-they offered the newspaper at a price of Rs. 1.50 on weekdays. The Hindustan Times was forced to reduce its prices from Rs.2.50 per copy to Rs.1.50 per copy on weekdays. When Hindustan Times was celebrating its 75 years of service, they offered the newspaper at Rs.1/-weekdays. The Times of India responded by matching the price cut.

There are many factors which work behind statistical facts and these forces operating together. For example, statistics of employment in an economy are affected by demand and supply of labour force, working conditions, production methods used etc. Similarly if the average weight of class is 56 kg then there are many factors responsible for it- geographical, genetic, gender etc.

(l) Diminishing returns determines the shape of both of these curves.


(ii) When marginal product is rising, marginal cost is falling.
(iii) When diminishing returns occur, marginal product begins falling and marginal cost begins rising.

Random Sampling
There are two methods of random sampling.
1. Unrestricted Random Sampling
2. Restricted random sampling.
Unrestricted Random Sampling
1. Lottery Method
2. Use of Random Number Tables
Restricted Random Sampling
1. Stratified Sampling/Mixed Sampling
2. Cluster Sampling
3. Systematic Sampling
Non-Random Sampling
1. Quota Sampling
2. Judgment Sampling / Purposive Sampling / Deliberate Sampling
3. Convenience Sampling /Availability Sampling
Cluster sampling is a sampling technique used when "natural" but relatively homogeneous groupings are evident in a statistical population. It is often used in marketing research. In this technique, the total population is divided into these groups (or clusters) and a simple random sample of the groups is selected. Then the required information is collected from a simple random sample of the elements within each selected group. This may be done for every element in these groups or a subsample of elements may be selected within each of these groups. A common motivation for cluster sampling is to reduce the total number of interviews and costs given the desired accuracy. Assuming a fixed sample size, the technique gives more accurate results when most of the variation in the population is within the groups, not between them.

Price Elasticity of Supply (ES)= \(\frac { \triangle Q }{ \triangle P } \times \frac { P }{ Q } \)
\(2.5=\frac { \triangle Q }{ 1 } \times \frac { 5 }{ 300 } \),i.e.,\(\triangle \)Q=150
As price decreases, than quantity supplied will also decrease. It means, New Quantity = Original Quantity (Q) - Change in Quantity (\(\triangle \)Q] = 300 - 150 = 150 units New Quantity = 150 units

Economics is a science but it is different from physical sciences. It is a social science i.e. it is a science dealing with human beings. Unlike physical sciences, Economics is based on assumptions. Since our subject matter is human being whose behaviour is very unpredictable, economics assumes man to behave rationally. However, many a time, a man is not rational but emotional and in such cases economics laws do not operate. Similarly, there are many factors which affect a phenomenon simultaneously. But for simplicity sake, we assume other things to remain same which they may not.

(a)

(b)

New TR curve Will be a steeper straight line as the one in perfect competition

Percentage change in price \(={\triangle P\over P}\times 100={1\over4}\times 100=25\%\)
\(PED={Percentage\ change\ in\ Quantity\ demended \over Percentage\ change\ in\ price}\)
\(={[-]20\%\over 25\%}=[-]0.8\)
Negative Sign of ED indicates that inverse relationship between price and quantity demanded. PED = 0.8 [Less than unitary elastic demand or inelastic demand].

The conditions are:

(i) Price of substitute goods rises.
(ii) Price of complementary goods falls.
(iii) Income of a consumer rises in case of normal goods.
(iv) Income of a consumer falls in case of inferior goods.
(v) When the preferences are favourable.

All economies whether developed or developing, have similar central problem because one or more of their resources (land, labour, capital and entrepreneurship) are limited and these resources can be put to alternative uses. The wants of the economies are unlimited. Therefore all economies have to face the basic economic problem of choice (what to produce, how to produce and for whom to produce).

(i) When MU decreases, TU increases at a diminishing rate. (As shown in figure till consumption level OQ).
(ii) When MU is zero, TU is maximum at P.
(iii) When MU is negative, TU starts diminishing.