Use of Statistical Tools | CBSE Class 11 Economics Notes

This note covers planning an economic project, choosing a target group, collecting and presenting data, designing a toothpaste survey, calculating averages and variability, interpreting consumer preferences, and preparing conclusions and a bibliography.

How do statistical tools help in planning an economic project?

Statistics involves collecting, organising, presenting and analysing data to reach meaningful conclusions. Data are the information collected for investigation. Statistical tools help examine economic activities such as production, consumption, distribution, banking, insurance, trade and transport.

A project is an investigation of a chosen problem or area of study. Conducting a survey and preparing a report helps analyse relevant information and suggest improvements in a product or system. The starting point is a clear objective, meaning what the investigation seeks to find out.

What sequence should the project follow?

1. Identify the problem: decide what you want to study and use that objective to guide the collection and processing of information.
2. Choose the target group: identify the people on whom the investigation will focus.
3. Collect data: decide whether the objective requires information collected first hand, information already available, or both.
4. Organise and present: arrange the collected information in tables and suitable diagrams.
5. Analyse and interpret: use statistical measures to examine averages, variability (how much values differ) and relationships, where relationships exist.
6. Conclude: draw meaningful conclusions from the results and, if possible, suggest future prospects or improvements.
7. Prepare the bibliography: record the details of secondary sources, meaning existing materials consulted, in the project bibliography, or source list.

This sequence connects the purpose of the investigation to its final report. A question about consumers' preferences requires information about consumers; a question about household water problems requires information from the households concerned. Collection and analysis therefore follow the chosen objective.

Which economic issues can become projects?

Possible studies include a coordinated transport system; a bank-loan proposal for a cottage industry making dhoop, agarbatti, candles or jute products; and the effect of advertisements on product sales. Other topics include literacy and school dropouts, overcharging, drinking water, women's participation in employment schemes, and health and sanitation.

Further possibilities are food adulteration, a polio immunisation programme, saving habits examined through income and expenditure, and farming practices and farmers' problems. Overcharging here means charging above the Maximum Retail Price, or MRP, the maximum retail price marked for the product.

How are the target group and method of data collection chosen?

Definition: The target group consists of the people on whom a study focuses. Its selection helps determine which questions are appropriate for the investigation.

For a project concerning cars, the target group will mainly be middle-income and higher-income groups. A study of a consumer product such as soap targets rural and urban consumers. For safe drinking water, the target group can include both rural and urban populations.

The population consists of all individuals or units about whom information is sought. A sample is a representative set selected from that population. The population and sample must be chosen carefully, and any sampling method must suit the investigation.

How do primary and secondary data differ?

Primary data are collected first hand for the enquiry. They may be collected using a questionnaire, a prepared list of questions answered by respondents, or an interview schedule, a question list used during an interview. A respondent is the person supplying the answers.

Collection can involve personal interviews, postal surveys, telephone enquiries or email. A postal questionnaire must include a covering letter explaining the purpose of the enquiry. The objective also guides the investigation of the target group's size and characteristics.

Secondary data are information already available from other sources. They can be used provided they suit the requirement. They are usually used when time, money and manpower are scarce and the required information is easily available.

The objective can require primary data, secondary data or both. For a household investigation into female literacy at primary and secondary levels, or the consumption of a particular soap brand, first-hand enquiries provide the relevant household information.

Suitability is therefore central to choosing a source. Easy availability alone does not establish that information answers the question being investigated. The choice of target group, data source and collection method must remain connected to the same objective.

How should the toothpaste survey questionnaire be designed?

The sample project concerns X, the label used for a young entrepreneur who wants to establish a toothpaste factory. An entrepreneur here is someone proposing to start a business. Advising X can begin with studying consumers' tastes, monthly toothpaste expenditure and other relevant information.

A questionnaire must generate the information the study needs. The proposed investigation seeks average monthly expenditure, brands currently in demand, attitudes towards those brands, preferences about ingredients, major media influences, and the relationship between income and these factors. A brand identifies a product; ingredients are its constituent substances; media are channels conveying information.

What information does the questionnaire request?

1. Personal and family details: name, sex, ages of family members in years, total family size, monthly family income and whether the residence is urban or rural.
2. Main occupation: whether the main breadwinner, the principal income earner, is in service, a professional, a manufacturer, a trader or another occupation.
3. Existing toothpaste use: whether the family uses toothpaste, the brand used, and the number of 100 gram packs used each month.
4. Qualities and satisfaction: the qualities considered essential in toothpaste and whether the family is satisfied with its present toothpaste.
5. New-product preferences: willingness to try a new toothpaste and the features desired in it.
6. Sources of information: cinema, exhibitions, internet, magazines, newspapers, radio, sales representatives, television or another source.

The feature questions offer plain, gel, antiseptic, flavoured, “Carries Protection”, fluoride and other options. Plain means without the listed special features; gel describes its gel form; antiseptic refers to action against microorganisms; flavoured refers to added taste. Fluoride is a fluoride-containing ingredient.

“Carries Protection” refers to protection against dental caries, or tooth decay. These are survey categories, rather than claims establishing the effectiveness of any product.

Why does the design of each question matter?

The questions about essential qualities and desired features allow more than one option to be ticked. Questions about satisfaction and willingness to try a new toothpaste offer yes or no answers. Different questions therefore collect different kinds of information.

A questionnaire already tried and tested, perhaps for a similar study, could be modified to suit the requirements. Otherwise, prepare one that asks for all the required information. The method used for another project will depend on its subject.

Monthly expenditure means money spent during a month; income means money received during the period under study. Recording income as well as preferences supports the proposed investigation into relationships between income and consumer behaviour.

How are collected data organised, presented and interpreted?

Organisation means arranging collected information into a usable form. Tabulation presents it in rows and columns. For the toothpaste project, separate tables describe age, family size, income, occupation, brand choice, satisfaction, ingredients and sources of information.

A frequency is the number of observations in a category or class. An observation is one recorded item of data. A frequency distribution arranges values into classes and gives the number of observations in each class.

What do diagrams contribute?

A bar diagram uses bars to represent the values of categories. A pie diagram divides a circle into parts representing categories. A histogram represents a grouped frequency distribution. These are ways of presenting information so that the pattern can be examined.

Presentation is followed by analysis, the examination and explanation of the economic problem, and interpretation, explaining what the statistical results mean. A chart displays the data; the accompanying observation expresses the finding relevant to the investigation.

Which statistical tools answer which questions?

Measures of central tendency, such as the mean, describe an average. The mean is the arithmetic average. Measures of dispersion, such as standard deviation, describe variability. Standard deviation measures the spread of values around their mean.

Correlation examines the relationship between variables, if it exists. A variable is a measurable quantity that can take different values, such as income or expenditure. Recording both quantities prepares the information needed to examine a possible relationship.

The choice of tool follows the purpose of analysis: average expenditure, variation in income and relationships between variables are different questions. A project brings collection, tables, diagrams and statistical measures together to support meaningful conclusions about the chosen economic issue.

What does the sample reveal about location, age and family size?

The toothpaste survey covers 100 households. A household is the family unit used for collecting the survey information. The location distribution is 67% urban and 33% rural, where % means per hundred. The majority of users belonged to an urban area.

How are persons distributed by age?

The age distribution concerns persons, with a total of 500, whereas the overall sample size concerns households. The majority of persons surveyed belonged to the age group 20 to 50 years. Keep the unit being counted clear when interpreting each table.

The horizontal axis lists six age groups from Below 10 to Above 50. The vertical axis is labelled Family Members. The bars show 74, 56, 91, 146, 93 and 40, with the tallest bar for 30 to 40 years.

See Fig. 8.1 in your NCERT textbook

How large are the surveyed families?

The majority of families surveyed have 3 to 6 members. This observation brings together the 3 to 4 and 5 to 6 categories. It describes the surveyed families; the age table separately describes the persons belonging to them.

Family size appears on the horizontal axis and number of households on the vertical axis. Four bars represent 1 to 2, 3 to 4, 5 to 6 and Above 6 members, with heights 20, 40, 30 and 10.

See Fig. 8.2 in your NCERT textbook

Together, location, age and family size describe the composition of the sample. These details give a background to the subsequent findings about income, occupation and toothpaste preferences without confusing families with individual family members.

How are mean monthly income and its standard deviation calculated?

A class midpoint is the middle value of a class and represents its observations in grouped calculations. Let x denote this midpoint. The lower and upper class limits are the values marking the two ends of the class.

x = (lower class limit + upper class limit)/2

Let A be the assumed mean, a convenient approximate value for simplifying calculation; c the scaling divisor; and d′ the coded deviation, the midpoint's difference from A divided by c. For income, A is Rs 20,000 and c is Rs 5,000. Rs denotes rupees.

$d' = (x - A)/c$

Let f denote class frequency, here the number of households. The product fd′ is frequency multiplied by coded deviation; fd′² is frequency multiplied by its square. The symbol Σ means the sum across all classes.

The column totals are Σf = 100, Σfd′ = −40 and Σfd′² = 340. The majority of surveyed families have monthly income between Rs 10,000 and Rs 30,000.

How does coding lead to the mean?

Worked example 1. For the Rs 0 to Rs 10,000 income class with frequency 20, use midpoint Rs 5,000, assumed mean Rs 20,000 and divisor Rs 5,000 to find its coded deviation and frequency products.

Answer: d′ = (5000 − 20000)/5000 = −3. Its frequency is 20, so fd′ = −60 and fd′² = 180.

Write the arithmetic mean as Mean. Coding first calculates the average coded deviation, then multiplies by c to restore the monetary scale and adds A.

Mean = A + (Σfd′/Σf) × c

Worked example 2. Calculate mean monthly income using A = Rs 20,000, c = Rs 5,000, total frequency 100 and the total fd′ of −40.

Answer: Mean = 20000 + (−40/100) × 5000 = 20000 − 2000 = Rs 18,000 per household per month.

How is income variability calculated?

Let σ, pronounced sigma, denote standard deviation. The symbol √ means square root. In the formula, the square of the average coded deviation is subtracted from the average squared coded deviation.

σ = √[(Σfd′²/Σf) − (Σfd′/Σf)²] × c

Worked example 3. Find income standard deviation using Σfd′² = 340, Σfd′ = −40, Σf = 100 and c = Rs 5,000.

Answer: σ = √[(340/100) − (−40/100)²] × 5000 = √(3.40 − 0.16) × 5000 = √3.24 × 5000 = 1.8 × 5000 = Rs 9,000.

The chart labelled Histogram has Income on the horizontal axis and number of families on the vertical axis. Four columns show frequencies 20, 40, 30 and 10; the 40-family column is tallest.

See Fig. 8.3 in your NCERT textbook

How is the monthly family budget on toothpaste analysed?

The monthly family budget on toothpaste records household expenditure on toothpaste during a month. Its grouped distribution uses expenditure amounts and the number of households in each class. Income and toothpaste expenditure are different variables, even though both are measured in rupees.

For this calculation, the assumed mean A is Rs 100 and the divisor c is Rs 40. The same symbols x, f and d′ retain their meanings: midpoint, frequency and coded deviation. Thus d′ is calculated as (x − 100)/40.

The column totals are Σf = 100, Σfd′ = 10 and Σfd′² = 90. The expenditure classes represent money spent on toothpaste, while frequencies indicate how many households fall within each class.

How is average toothpaste expenditure found?

Worked example 4. Calculate mean monthly expenditure on toothpaste using A = Rs 100, c = Rs 40, total frequency 100 and total fd′ of 10.

Answer: Mean = 100 + (10/100) × 40 = Rs 104 per household per month.

The mean expresses expenditure as a single average for the surveyed households. The distribution still shows the different expenditure classes. The standard deviation was Rs 35.60.

Interpretation must preserve the time period and the unit being studied. The Rs 104 figure refers to monthly expenditure per household, rather than the price of a toothpaste pack or expenditure per person. The questionnaire separately asks how many 100 gram packs a family uses each month.

Keeping these distinctions clear connects the statistical calculation to the entrepreneur's information needs. The investigation concerns household spending as well as brand preferences, desired features and media influences; an average expenditure figure addresses one part of that wider enquiry.

What do occupation and brand choice show about the surveyed households?

Occupational status describes the work category associated with the family. The occupation table distinguishes service, professional work, manufacture, trading and other work. It provides another part of the sample's background before preferences are interpreted.

The majority of surveyed families were either service class or traders. These are the two occupation groups brought together in the observation. The statement concerns the surveyed families and accompanies their recorded occupational distribution.

A pie diagram divides the occupations into sectors labelled 5%, 10%, 15%, 30% and 40%. Its legend identifies Professional, Manufacturer, Any other, Service and Trader; the trader sector is the largest.

See Fig. 8.4 in your NCERT textbook

Which toothpaste brands were preferred?

A brand is the name identifying a product offered for sale. The table records the number of households using each listed toothpaste brand, together with an “Any other” category.

Pepsodent, Colgate and Close-up were the most preferred brands among the surveyed households. Their household counts are 20, 18 and 12 respectively. This is a finding about the sample and its existing toothpaste use.

Brand use and occupation answer different questions. Occupation describes the families; brand use identifies the products they currently choose. The questionnaire also asks whether users are satisfied, because the name of the toothpaste used is distinct from the user's attitude towards it.

How do selection reasons and satisfaction deepen the analysis?

The basis of selection means the considerations involved in choosing toothpaste. The survey includes advertisement, advice from a dentist, price, quality, taste, ingredients, standardised marking, trying a new product and the company's brand name.

Standardised marking refers here to a product mark indicating conformity to a standard. Ingredients are the substances included in the toothpaste. The table records these as considerations in product choice, alongside price and the other listed factors.

The majority of people selected toothpaste on the basis of standardised markings, quality, price and company brand name. This observation identifies the prominent selection factors without replacing the individual values shown in the table.

What does satisfaction add to brand-use information?

Satisfaction indicates whether users are content with their toothpaste. The satisfaction table separates satisfied and unsatisfied users for each listed brand. “Close up” is the label used in this table.

Amongst the most used toothpastes, the percentage of dissatisfaction was relatively less. Some users of these brands were nevertheless unsatisfied, as the table shows. Preference for a brand does not mean that every user is satisfied with it.

What do ingredient preferences and media influence reveal?

Preferences are the features consumers favour. The ingredient-preference table groups the responses into plain, gel, antiseptic, flavoured, “Carries protective” and fluoride categories. “Carries protective” refers to tooth-decay protection.

The majority of people preferred gel and antiseptic-based toothpastes over the others. These responses concern desired features, while the brand table identifies products already used. The questionnaire allows more than one option in its feature questions.

Which sources influenced families?

Media influence concerns the information channels through which families learn about toothpaste. The project records television, newspapers, magazines, cinema, sales representatives, exhibition stalls and radio. A sales representative is a person presenting or promoting the product to prospective buyers.

Seven bars compare television, newspaper, magazine, cinema, sales representative, exhibits stall and radio. The vertical axis shows Families Influenced. The bars carry values 47, 30, 20, 25, 15, 10 and 18 respectively.

See Fig. 8.5 in your NCERT textbook

The majority of people came to know about the product either through television or newspaper. Television is the most popular medium for reaching people in the project's conclusion. These observations connect the information-channel findings to the proposed business study.

The media table and ingredient table address separate information needs. One concerns how people hear about the product; the other concerns the kinds of toothpaste they prefer. Both contribute to advising the entrepreneur alongside expenditure, brand use and satisfaction.

How should conclusions and the bibliography complete the report?

A conclusion brings together meaningful findings after the results have been analysed and interpreted. It should follow the information collected. If possible, try to predict future prospects and offer suggestions concerning growth or government policies on the basis of the information collected.

What findings belong in the toothpaste report?

The report brings together the urban majority, the prominence of families with 3 to 6 members, and the main occupations of service and trading. The majority of surveyed families have monthly incomes between Rs 10,000 and Rs 30,000.

It also brings together about Rs 104 of monthly toothpaste expenditure per household, the preference for Pepsodent, Colgate and Close-up, and the preference for gel or antiseptic-based toothpastes. A lot of people are influenced by advertisements, with television the most popular medium for reaching them.

Each finding has a role in the investigation: household characteristics describe the sample, expenditure describes spending, brand and ingredient choices describe preferences, and media information describes how people learn about products. The report connects these findings to the original objective.

What is included in a bibliography?

A bibliography lists details of all secondary sources used in developing the project. Such sources may include magazines, newspapers and research reports. It records the materials consulted in addition to the information collected through the survey.

The complete investigation therefore links a clear objective, carefully selected population and sample, suitable data, a questionnaire or interview schedule, statistical analysis and meaningful conclusions. Its method must suit its own subject rather than mechanically reproduce the toothpaste project's approach.

Glossary

• Objective — The purpose of an investigation, guiding what information should be collected and analysed.
• Target group — The people on whom a study focuses when preparing questions and collecting information.
• Population — All individuals or units about whom information is sought for the investigation.
• Sample — A representative set of individuals or units selected from the population for study.
• Primary data — Information collected first hand for an enquiry through suitable methods such as interviews.
• Secondary data — Information already available from sources such as magazines, newspapers and research reports.
• Questionnaire — A prepared list of questions on the subject of enquiry for respondents to answer.
• Frequency — The number of observations occurring in a particular category or class of a distribution.
• Class midpoint — The middle value of a class, representing its observations in grouped statistical calculations.
• Assumed mean — An approximate value chosen to make the calculation of an average more convenient.
• Coded deviation — The difference between a class midpoint and the assumed mean, divided by a scaling divisor.
• Standard deviation — A statistical measure describing the spread of values around their arithmetic mean.
• Correlation — A statistical tool for examining the relationship between variables, if such a relationship exists.
• Bibliography — A list giving details of secondary sources used in developing the project report.

Common errors and misconceptions

• Misconception: Every project should use the same target group. Correct: The target group depends on the objective; cars mainly concern middle-income and higher-income groups, while soap studies target rural and urban consumers.
• Misconception: Readily available secondary data are automatically suitable. Correct: They can be used provided they meet the enquiry's requirements, even when time, money and manpower are scarce.
• Misconception: The sample contains 500 households. Correct: It contains 100 households; the age table counts 500 persons. Keep the observation unit attached to each figure.
• Misconception: Rs 104 is the price of one toothpaste pack. Correct: It is average monthly toothpaste expenditure per household; the questionnaire separately asks about 100 gram packs used.
• Misconception: Every feature question permits just one answer. Correct: Questions about essential qualities and desired new-product features explicitly allow more than one option to be selected.
• Misconception: Popular toothpaste brands have no dissatisfied users. Correct: Amongst the most used toothpastes, the percentage of dissatisfaction was relatively less; this does not mean dissatisfaction was absent.
• Misconception: A report is complete once its tables are prepared. Correct: Results must also be analysed and interpreted, conclusions drawn, and the details of secondary sources recorded in the bibliography.

Exam-style questions with model answers

Q1. What is a target group, and why should it be identified before preparing a questionnaire? [2 marks]

1. A target group consists of the people on whom the investigation focuses.
2. Identifying it helps frame appropriate questions that match the study's objective and the people being investigated.

Q2. Explain three considerations when choosing how to collect data for an economic project. [3 marks]

1. The survey objective determines whether the investigation needs primary data collected first hand, secondary data already available, or a combination of both methods.
2. Secondary data can be used provided they suit the requirements. They are usually used when time, money and manpower are scarce and information is readily available.
3. If sampling is used, its method must suit the investigation, with the population and sample chosen carefully.

Q3. For a grouped monthly-income distribution, the assumed mean is Rs 20,000, scaling divisor Rs 5,000, total household frequency 100 and sum of frequency multiplied by coded deviation −40. Calculate and interpret mean income in four steps. [4 marks]

1. The coded-deviation method finds the mean by adding to the assumed mean the average coded deviation multiplied by the scaling divisor.
2. The average coded deviation is the supplied product sum divided by total frequency: −40/100.
3. Substituting gives mean income = 20000 + (−40/100) × 5000 = 20000 − 2000 = Rs 18,000.
4. The surveyed households therefore have average monthly income of Rs 18,000 per household.

Q4. A monthly toothpaste-expenditure distribution has assumed mean Rs 100, scaling divisor Rs 40, total frequency 100 and sum of frequency multiplied by coded deviation 10. Calculate and interpret its mean expenditure. [2 marks]

1. Mean expenditure = 100 + (10/100) × 40 = Rs 104.
2. This is the average amount spent on toothpaste per household per month.

Q5. For a household monthly-income distribution, the sum of frequency multiplied by squared coded deviation is 340; the sum of frequency multiplied by coded deviation is −40; total frequency is 100; and the scaling divisor is Rs 5,000. Calculate standard deviation in four steps. [4 marks]

1. Standard deviation is the square root of the difference between the average squared coded deviation and the square of the average coded deviation, multiplied by the divisor.
2. The average squared coded deviation is 340/100 = 3.40. The square of the average coded deviation is (−40/100)² = 0.16.
3. The difference is 3.24, whose square root is 1.8. Multiplying by 5000 gives Rs 9,000.
4. Thus the standard deviation of monthly household income is Rs 9,000, describing income variability around its mean.

Q6. Outline six stages of an economic project, from identifying its objective to reaching conclusions. [6 marks]

1. Identify the problem or area of study clearly. The objective guides the collection and processing of information for the investigation.
2. Choose the target group on which attention will focus. This helps frame appropriate questions for the people being studied.
3. Collect primary data, secondary data or both, according to the objective. Ensure that any sampling method suits the investigation.
4. Organise and present the collected information through tables and suitable diagrams, such as bar diagrams or pie diagrams.
5. Analyse and interpret the data using tools that examine averages, variability and relationships between variables, if such relationships exist.
6. Draw meaningful conclusions. If possible, suggest future prospects and recommendations about growth or government policies based on the collected information.

Q7. An entrepreneur wants to establish a toothpaste factory. State five kinds of information a consumer questionnaire should collect to investigate expenditure, brand demand, attitudes, ingredients and media influence. [5 marks]

1. Collect information on monthly toothpaste expenditure so that average household expenditure can be established as part of the proposed product study.
2. Ask which toothpaste brands are currently used, providing information about the brands that consumers already demand in the surveyed households.
3. Ask whether consumers are satisfied with their current toothpaste, so their attitudes towards the brands used can be examined.
4. Ask about preferred ingredients and desired toothpaste qualities, allowing more than one feature where the question offers multiple selections.
5. Ask about information sources such as television, newspapers, cinema and radio to investigate the major media influences on consumers' demand.

Q8. A survey reports 100 households, 67% urban and 33% rural. Its family-size counts are: 1 to 2 members, 20 families; 3 to 4, 40; 5 to 6, 30; above 6, 10. State three findings about the sample unit, location and majority family-size range. [3 marks]

1. The overall sample consists of 100 households. The family-size frequencies count families, while the category labels describe the number of members belonging to each family.
2. The majority of the surveyed households are urban: 67% are urban and 33% are rural.
3. The majority of surveyed families have 3 to 6 members, covered by the 3 to 4 and 5 to 6 categories with frequencies 40 and 30.

Key takeaways

• A clearly identified objective guides the target group, the information collected and the analysis undertaken in an economic project.
• Primary and secondary data may be used separately or together, provided the chosen information meets the investigation's requirements.
• A questionnaire must obtain the required information, and a tested questionnaire may be suitably modified for another study.
• Tables and diagrams organise the survey results; averages, dispersion and correlation help analyse different aspects of those results.
• The toothpaste sample contains 100 households, while its age-distribution table records 500 persons belonging to the surveyed families.
• Mean monthly household income is Rs 18,000, and average monthly toothpaste expenditure is Rs 104 per household.
• Pepsodent, Colgate and Close-up were the most preferred brands; gel and antiseptic-based toothpastes were preferred over the others.
• Conclusions must follow analysis and interpretation, while a bibliography records the secondary sources used to develop the project.

Test yourself

What should come before collecting data for a project?

Clearly identify the problem or area of study and the objective of the investigation.

What must accompany a postal questionnaire?

A covering letter giving details about the purpose of the enquiry must accompany it.

When are secondary data usually used?

They are usually used when time, money and manpower are scarce and suitable information is easily available.

How do mean, standard deviation and correlation differ in purpose?

Mean describes an average, standard deviation describes variability, and correlation examines a relationship between variables if it exists.

What are the sample size and total age-table count in the toothpaste survey?

The sample covers 100 households, and the age-distribution table records a total of 500 persons.

Which brands were most preferred in the surveyed households?

Pepsodent, Colgate and Close-up were the most preferred toothpaste brands in the surveyed households.

Which medium was most popular for reaching people in the project's conclusion?

Television was the most popular medium for reaching people in the toothpaste project's conclusion.

What should the bibliography record?

It should give details of all secondary sources used, including magazines, newspapers and research reports.