Statistics: Definition, Scope and Limitations | ISC Class 11 Economics Notes

This note covers the meaning and definition of Statistics as a subject, its scope in Economics (consumption, production and distribution), the difference between quantitative and qualitative economic data, the importance of Statistics in understanding and solving economic problems, and the limitations of statistical methods.

What do Economics and Statistics have to do with each other?

Every household and every producer faces scarcity: wants are unlimited, but the resources available to satisfy them, such as land, labour and money, are limited and have alternative uses.

Because resources are scarce, people and societies must choose which wants to satisfy first and how to use the resources they have. This problem of choice under scarcity is the starting point of the subject of Economics.

Definition: Economics. "Economics is the study of how people and society choose to employ scarce resources that could have alternative uses in order to produce various commodities that satisfy their wants and to distribute them for consumption among various persons and groups in society."

Alfred Marshall, one of the founders of modern economics, described this subject as the study of "man in the ordinary business of life", meaning the day-to-day activities of buying, selling, producing and earning a living.

To study these activities properly, an economist needs reliable facts, called economic data, about consumption, production and distribution.

Collecting, organising and interpreting such facts in a systematic way is the task of Statistics, which is why Statistics has become a basic tool used in modern Economics.

What is Statistics?

Definition: Statistics. "Statistics deals with the collection, analysis, interpretation and presentation of numerical data." It is a branch of mathematics and is also used in disciplines such as accounting, economics, management, physics, finance, psychology and sociology.

In what two senses is the word statistics used?

The word statistics is used in two senses, and a full definition covers both.

• Plural sense (statistical data): statistics means numerical facts collected about a subject, such as the statistics of rice production, prices or population. Horace Secrist described statistics in this sense as "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".
• Singular sense (statistical methods): Statistics means the science or subject that deals with those facts. Croxton and Cowden defined it in this sense as "the collection, presentation, analysis and interpretation of numerical data".

Not every number is statistics in the plural sense. A single figure, such as one person's height, is not; a set of related figures collected for a purpose, such as the heights of all students in a class compared with each other, is. Secrist's definition therefore stresses that data must be aggregates, numerically expressed, affected by many causes, collected systematically for a predetermined purpose, and comparable with each other.

What kinds of data does Statistics use in Economics?

Within Economics, Statistics is concerned specifically with data drawn from economic activities such as prices, production, incomes and taxes. Most economic data of this kind are quantitative data, that is, facts that can be expressed directly as numbers.

For example, a statement such as the production of rice in India has increased from 39.58 million tonnes in 1974-75 to 106.5 million tonnes in 2013-14 is quantitative data.

Economics also makes use of qualitative data. These describe attributes of a person or group, such as gender, health or skill, that are important to record accurately even though they cannot be measured directly in numbers.

Qualitative attributes are often expressed in terms of degrees, for example unskilled, skilled or highly skilled, and such qualitative information is then collected and stored systematically, in the same way as quantitative information such as prices and incomes.

Collecting the data is the first step; after that, the subject matter of Statistics involves three further steps: presenting the data in tabular, diagrammatic and graphic forms; summarising the data by calculating numerical indices such as the mean, variance and standard deviation that represent the broad characteristics of the data; and finally analysing and interpreting the data.

What is the scope of Statistics in Economics?

Economics is traditionally discussed in three parts, and Statistics is used within each of them to collect and analyse the facts needed:

1. Consumption: how a consumer decides what to buy, given a fixed income, many alternative goods and known prices.
2. Production: how a producer decides what and how much to produce for the market, using the limited resources available, which have alternative uses.
3. Distribution: how the national income, that is the total income arising from what has been produced in a country (its Gross Domestic Product or GDP), is divided among wages and salaries, profits and interest.
4. Beyond these three conventional divisions, modern Economics also studies special problems facing a country, such as poverty, disparities in income between the rich, the middle class and the poor, illiteracy and unemployment, and the economic cost of disasters such as earthquakes or disease outbreaks.

Studying any of these areas requires numerical facts in a systematic form, which is exactly what Statistics provides.

Any activity undertaken for a monetary gain, such as buying, selling, producing, or being an employer or employee, is called an economic activity, and the numerical record of such activities forms economic data.

Without data on the factors underlying an economic problem, no analysis of that problem, and no policy to solve it, is possible.

Why is Statistics important in Economics?

Statistics is described as an indispensable tool for an economist because it helps in several distinct ways:

1. Finding causes. Using qualitative and quantitative facts, Statistics helps an economist find the causes behind a problem, for example explaining the hardships of poverty in terms of unemployment, low productivity or backward technology.
2. Making facts precise. Statistics presents economic facts in an exact and definite form. Stating that 310 people died in an earthquake is more factual and convincing than the vague statement that hundreds of people died.
3. Condensing mass data. Statistics summarises a very large mass of data into a few numerical measures, such as the mean or variance, so that, for instance, one summary figure like average income can represent the incomes of a very large number of people.
4. Finding relationships. Statistical methods are used to check whether a relationship exists between economic factors, for example between the price of a commodity and the demand for it, or between average income and consumption expenditure, and to test whether an assumed relationship is valid.
5. Prediction. Statistics helps predict changes in one economic factor due to changes in another, such as the impact of today's investment on future national income, using data on past or recent consumption obtained through surveys.
6. Policy formulation. Because plans require knowledge of future trends, for example how much an economy should produce in a future year, statistical tools help formulate appropriate policies, such as deciding how much oil a country should import based on its expected domestic production and expected demand.

Statistics is also used to evaluate the effect of a policy once it has been applied, for example whether a family planning policy is effectively checking population growth, and plays a role in decision making on problems such as rising prices, population growth and unemployment.

What are the limitations of Statistics?

Statistics is a powerful tool, but it has well recognised limitations that an economist must keep in mind.

• Statistics generally deals with aggregates and groups rather than with a single individual case, so its conclusions apply to a group on average and may not hold for every individual within it.
• Qualitative characteristics, such as honesty, beauty or intelligence, cannot be measured directly; they can only be studied statistically after being converted into degrees or scores, which is an approximation.
• Statistical conclusions are true only on average and in the long run, not as exact and certain as mathematical truths, so they must be interpreted with care.
• Statistics can be misused or misinterpreted, especially by persons without expert knowledge, which can lead to wrong conclusions and wrong decisions.

The point that statistical methods are no substitute for common sense is made through a well known illustration: a family of four once set out to cross a river.

The father knew the average depth of the river, and calculated that the average height of his family members was greater than that average depth, so he thought they could cross safely.

In the event, some members of the family, the children, drowned while crossing, because an average depth does not describe the depth at every point of the river, and a person's height does not determine whether they can survive at the deepest point.

This illustration raises the question of whether the fault lies with the statistical method of calculating averages, or with the misuse of the average once it was calculated.

The lesson usually drawn is that statistical results must always be interpreted sensibly and applied to the situation they actually describe.

Going beyond the syllabus

The distinction between economic activities and non-economic activities is useful background to the study of Statistics in Economics. An activity undertaken for monetary gain, such as a farmer growing a crop to sell, a shopkeeper selling goods for profit, or an employee working for wages, is an economic activity.

Activities undertaken without any monetary motive, such as helping a neighbour without charge, are not economic activities in this sense, even though they may still involve the use of scarce resources such as time.

Glossary

• Economics — the study of how people and society use scarce resources, which have alternative uses, to produce goods and distribute them among persons and groups.
• Statistics — the branch of study dealing with the collection, analysis, interpretation and presentation of numerical data.
• Scarcity — the condition in which the resources available to satisfy unlimited wants are limited, which is the root of all economic problems.
• Consumption — the purchase of goods by consumers to satisfy their various wants, given a fixed income and known prices.
• Production — the manufacture or raising of goods by producers for sale in the market using limited resources.
• Distribution — the division of national income among wages and salaries, profits and interest.
• Economic activity — any activity, such as buying, selling, producing or employment, undertaken for a monetary gain.
• Economic data — facts about economic activities, collected in numerical or systematic form, used to analyse economic problems.
• Quantitative data — data that can be measured directly and expressed as numbers, such as prices or production figures.
• Qualitative data — data describing attributes, such as gender or skill, that cannot be measured directly but can be graded and recorded systematically.
• Gross Domestic Product (GDP) — the total income or output arising from what has been produced within a country.
• Policy — a measure adopted, after analysing an economic problem, to help solve it.
• Average — a single summary figure, such as a mean, used to represent a mass of numerical data.
• Scope of Statistics — the range of economic areas, including consumption, production, distribution and special social problems, in which statistical methods are applied.
• Limitations of Statistics — the restrictions on statistical methods, such as dealing in aggregates, approximating qualitative facts, and the risk of misuse.

Common errors and misconceptions

• Misconception: Statistics only deals with quantitative, numerical facts. Correct: Statistics in Economics also uses qualitative data, such as attributes graded in degrees, collected and stored systematically.
• Misconception: Statistics itself solves economic problems. Correct: Statistics helps find causes and relationships and provides the facts needed; the actual policy to solve a problem is a separate decision made using that statistical information.
• Misconception: An average always describes every individual case accurately. Correct: An average is a summary figure true on average for a group; applying it to an individual case, as in the story of the family crossing the river, can be misleading.
• Misconception: Any activity that uses resources is an economic activity. Correct: Only activities undertaken for a monetary gain, such as buying, selling or working for wages, are called economic activities.
• Misconception: Statistics is a subject used only in Economics. Correct: Statistics is a branch of mathematics also used in accounting, management, physics, finance, psychology and sociology.
• Misconception: Statistical conclusions are as certain as mathematical facts. Correct: Statistical conclusions are generally true on average and in the long run, not with the same certainty as a mathematical proof.
• Misconception: Scarcity means that something is simply unavailable. Correct: Scarcity means resources are limited relative to unlimited wants and have alternative uses, forcing a choice among competing uses.

Exam-style questions with model answers

Q1. State the subject matter of Statistics. [1 mark]

1. Statistics deals with the collection, analysis, interpretation and presentation of numerical data, and is used in Economics to study economic facts systematically.

Q2. Distinguish between quantitative data and qualitative data, giving one example of each. [2 marks]

1. Quantitative data are facts that can be measured directly and expressed as numbers, for example rice production figures measured in tonnes.
2. Qualitative data describe attributes of a person or group, such as gender or skill level, that cannot be measured directly but can be recorded as degrees, for example unskilled, skilled or highly skilled.

Q3. Why is scarcity said to be the root of all economic problems? [2 marks]

1. Wants are unlimited, but the resources used to satisfy them, such as land, labour and money, are limited in availability.
2. Because the same resources have alternative uses, people and producers must choose which wants to satisfy and which goods to produce, and this problem of choice is the economic problem.

Q4. Explain the scope of Economics in terms of consumption, production and distribution. [4 marks]

1. Consumption is the study of how a consumer, given a fixed income and known prices, decides what goods to buy among the alternatives available.
2. Production is the study of how a producer decides what and how much to produce for the market, using resources that have alternative uses.
3. Distribution is the study of how the national income, or GDP, generated from production is divided among wages and salaries, profits and interest.
4. These three divisions together require systematic numerical facts, which is why Statistics has become essential to studying Economics properly.

Q5. Explain any four ways in which Statistics helps an economist. [4 marks]

1. Statistics helps find the causes behind an economic problem, for example explaining poverty in terms of unemployment or low productivity.
2. Statistics presents economic facts in a precise, exact form, which is more convincing than vague statements.
3. Statistics condenses a large mass of data into a few summary measures, such as an average, making it possible to describe a group without listing every individual figure.
4. Statistics helps verify whether a relationship exists between economic factors, such as between price and demand, and helps predict future changes, for example the effect of today's investment on future national income.

Q6. Discuss the limitations of Statistics as a tool of economic analysis, illustrating your answer with a suitable example. [6 marks]

1. Statistics generally studies aggregates or groups, so its conclusions describe the group on average and may not hold true for every individual case within it.
2. Qualitative attributes, such as intelligence or honesty, cannot be measured directly and can only be approximated by converting them into degrees or scores.
3. Statistical conclusions are true only on average and in the long run, unlike the exact certainty of a mathematical proof.
4. Statistics can be misused, particularly by persons without expert knowledge, leading to wrong conclusions.
5. This can be illustrated by the story of a family that tried to cross a river after the father calculated that the average height of the family was greater than the average depth of the river, and concluded they could cross safely.
6. In fact, the children drowned, because the average depth did not describe the depth at every point of the river, showing that statistical results must be interpreted sensibly and applied to the exact situation they describe, and are no substitute for common sense.

Q7. Explain the importance of Statistics in the formulation of economic policy, with examples. [6 marks]

1. Formulating any economic policy requires knowledge of future trends, for example how much an economy should produce in a future year.
2. Such predictions can be based either on subjective judgement or, more reliably, on statistical tools applied to data on past or recent consumption obtained through surveys.
3. One example given is deciding how much oil a country should import, which depends on the expected domestic production of oil and the likely future demand for it, both of which can only be estimated statistically.
4. Another example is checking whether a policy such as family planning is actually effective in controlling population growth, which again requires statistical evaluation of the data before and after the policy.
5. Statistics therefore helps not only in deciding what policy to adopt, but also in evaluating the impact of a policy once it has been applied.
6. Without the use of Statistics, the facts needed to decide and evaluate such policies, such as expected production, likely demand or the effect of a scheme, cannot be determined, so sound policy making depends on statistical methods.

Key takeaways

• Scarcity, the condition that unlimited wants face limited resources with alternative uses, is the root of all economic problems and the starting point of the study of Economics.
• Economics studies economic activities undertaken for monetary gain, organised traditionally into consumption, production and distribution.
• Statistics deals with the collection, analysis, interpretation and presentation of numerical data, and is a branch of mathematics also used in several other disciplines.
• Economics uses both quantitative data, which can be measured directly, and qualitative data, which describe attributes graded in degrees.
• The scope of Statistics in Economics covers consumption, production, distribution and special problems such as poverty, disparity and disaster costs.
• Statistics helps economists find causes, express facts precisely, condense mass data into summary measures, verify relationships, predict future trends and formulate policy.
• Statistics is also used to evaluate whether a policy has actually been effective in solving the problem it targeted.
• Statistics has limitations: it generally studies aggregates rather than individuals, approximates qualitative facts, gives conclusions true only on average, and can be misused if not interpreted with common sense.

Test yourself

What is the definition of Statistics?

Statistics deals with the collection, analysis, interpretation and presentation of numerical data, and is a branch of mathematics also used in other disciplines such as economics and management.

Give one example of quantitative data and one example of qualitative data.

Rice production rising from 39.58 million tonnes to 106.5 million tonnes is quantitative data; a person's skill being graded as unskilled, skilled or highly skilled is qualitative data.

Name the three conventional divisions through which Economics is studied.

Economics is conventionally studied through consumption, production and distribution.

How does Statistics help in predicting future economic trends?

Statistics uses data on past or recent consumption, often obtained through surveys, to predict changes in one economic factor, such as national income, due to changes in another, such as investment.

What lesson does the story of the family crossing the river teach about Statistics?

It teaches that an average is a summary figure true for a group, and applying it blindly to an individual case can be misleading, so statistical results must be interpreted with common sense.

Why can Statistics not study qualitative characteristics as directly as quantitative ones?

Qualitative characteristics, such as beauty or honesty, cannot be measured directly, so they can only be studied statistically after being converted approximately into degrees or scores.

Give one example of how Statistics helps in forming government policy.

Deciding how much oil to import depends on the expected domestic production and likely future demand for oil, both of which are estimated using statistical methods.