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NCERT · Class 11 · Statistics

Chapter 8: Use of Statistical Tools

Practice each question, then open the answer or worked solution.

Project activities

12 questions
Q1Written answer

Consider yourself as an advisor to Transport Minister who aims to bring about a better and coordinated system of transportation. Prepare a project report.

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Worked solution
GUIDED ANSWER Objective: to assess current transport facilities (buses, metro, autos, trains) and suggest a better, coordinated system. Target group: daily commuters — students, office-goers, traders — across both urban and rural routes. Data to collect (primary, by questionnaire): mode used, average daily travel time, waiting time, fare paid, frequency of service, level of crowding, and a satisfaction rating (1–5). Tools: tabulate responses; show modal share by a pie diagram and average waiting time by a bar diagram; compute the mean travel time and fare and the standard deviation to show how uneven service is; use correlation between waiting time and satisfaction. Conclusion: recommend, on the evidence, more buses on overloaded routes, integrated ticketing and better last-mile connectivity, then list your bibliography.
Q2Written answer

You may be working in a village cottage industry. It could be a unit manufacturing dhoop, agarbatti, candles, jute products, etc. You want to start a new unit of your own. Prepare a project proposal for getting a bank loan.

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Worked solution
GUIDED ANSWER Objective: to prepare a project proposal showing that a new cottage unit (say agarbatti) is viable, so a bank will sanction a loan. Target group / data: survey raw-material suppliers and existing units for cost data; survey shops/customers for demand. Use secondary data for market prices and government subsidy schemes (MUDRA/MSME). Tools: tabulate the estimated cost of land, machinery, raw material, labour and the expected monthly sales; show projected income vs expenditure as a bar diagram; compute the mean monthly profit and a simple break-even point; estimate the loan amount and repayment schedule. Conclusion: state the loan required, the projected returns and how the loan will be repaid, with a bibliography of the secondary sources used.
Q3Written answer

Suppose you are a marketing manager in a company and recently you have put up advertisements about your consumer product. Prepare a report on the effect of advertisements on the sale of your product.

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Worked solution
GUIDED ANSWER Objective: to measure whether advertisements have raised the sale of a consumer product. Target group: retailers and customers in the area where the advertisements ran. Data: monthly sales figures before and after the campaign (secondary data from company records); a customer survey on which advertisement they saw and where (TV, newspaper, internet). Tools: show monthly sales as a bar diagram; compute the mean sale before and after to see the rise; compute correlation between advertising expenditure and sales; show media reach by a pie diagram. Conclusion: state whether sales rose, which medium was most effective, and whether the campaign was worth its cost.
Q4Written answer

You are a District Education Officer, who wants to assess the literacy levels and the reasons for dropping out of school children. Prepare a report.

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Worked solution
GUIDED ANSWER Objective: to assess literacy levels in the district and find why children drop out of school. Target group: households with school-age children, plus schools, in selected villages/wards (use random sampling). Data: number of children enrolled vs out of school, gender, class at which they left, and reasons (poverty, child labour, distance, lack of toilets, early marriage). Tools: compute the literacy rate (a percentage); show reasons for dropping out as a bar diagram and gender split as a pie diagram; tabulate dropout by class. Conclusion: identify the main reasons and recommend measures (mid-day meals, free books, schools nearer to habitations), with a bibliography.
Q5Written answer

Suppose you are a Vigilance Officer of an area and you receive complaints about overcharging of goods by traders i.e., charging a higher price than the Maximum Retail Price (MRP). Visit a few shops and prepare a report on the complaint.

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Worked solution
GUIDED ANSWER Objective: to verify whether traders charge more than the MRP printed on goods. Target group: a sample of shops in the area and the customers buying from them. Data: for selected items, record the printed MRP and the actual price charged; note the type of shop and the item. Tools: tabulate ‘MRP vs price charged’; compute the mean overcharge per item and the percentage of shops overcharging; show overcharging item-wise as a bar diagram. Conclusion: report whether overcharging is common, which items and shops are involved, and recommend action (warnings, display of MRP, consumer awareness).
Q6Written answer

Consider yourself to be the head of Gram Panchayat of a particular village who wants to improve amenities like safe drinking water to your people. Address your issues in a report form.

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Worked solution
GUIDED ANSWER Objective: to study the availability of safe drinking water in the village and suggest improvements. Target group: all households of the village (a census is possible in a small village). Data: source of drinking water (tap, handpump, well, tanker), distance to the source, whether water is treated, and water-borne illnesses reported. Tools: show sources by a pie diagram; compute the mean distance to a water source; tabulate households with and without safe water; compute the percentage served. Conclusion: recommend new taps/handpumps, water testing and rainwater harvesting where the data show gaps, with a bibliography.
Q7Written answer

As a representative of a local government, you want to assess the participation of women in various employment schemes in your area. Prepare a project report.

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Worked solution
GUIDED ANSWER Objective: to assess how many women take part in government employment schemes (e.g. MGNREGA, self-help groups) and the obstacles they face. Target group: women of working age in the area. Data: number of women enrolled vs actually working, days of work, wages received, and reasons for low participation (household work, lack of awareness, safety, child care). Tools: compute the female participation rate (percentage); show participation scheme-wise by a bar diagram; compute the mean days of work and wage; show reasons for non-participation by a pie diagram. Conclusion: recommend awareness drives, crèches and timely wage payment, then list the bibliography.
Q8Written answer

You are the Chief Health Officer of a rural block. Identify the issues to be addressed through a project study. This may include health and sanitation problems in the area.

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Worked solution
GUIDED ANSWER Objective: to identify the main health and sanitation problems of a rural block. Target group: households of the block, with the local health centre as a secondary source. Data: households with/without toilets, drainage and clean water; common illnesses; access to a doctor or PHC; immunisation status of children. Tools: tabulate the data; show toilet/drainage coverage as a bar diagram and disease frequency as a pie diagram; compute the percentage of households with proper sanitation and the mean distance to a health centre. Conclusion: prioritise the worst problems (e.g. open defecation, unsafe water) and recommend toilets, awareness camps and a sub-centre, with a bibliography.
Q9Written answer

As the Chief Inspector of Food and Civil Supplies department, you have received a complaint about food adulteration in the area of your duty. Conduct a survey to find the magnitude of the problem.

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Worked solution
GUIDED ANSWER Objective: to find how widespread food adulteration is in the area. Target group: a sample of shops and vendors selling common items (milk, spices, oil, sweets). Data: for sampled items, record the result of a simple adulteration test (pass/fail), the item and the type of shop. Tools: tabulate item vs result; compute the percentage of adulterated samples; show adulteration item-wise as a bar diagram. Conclusion: report the magnitude (e.g. ‘X% of milk samples failed’), name the riskiest items, and recommend stricter checks and consumer awareness, with a bibliography.
Q10Written answer

Prepare a report on Polio immunisation programme in a particular area.

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Worked solution
GUIDED ANSWER Objective: to study the coverage and effectiveness of the polio immunisation programme in an area. Target group: households with children below five years. Data: number of eligible children, number immunised, number missed, awareness of pulse-polio dates, and reasons for missing doses (use secondary data from health records too). Tools: compute the immunisation coverage rate (percentage); show coverage area-wise by a bar diagram; tabulate reasons for missing and show them as a pie diagram. Conclusion: state how complete the coverage is, where gaps remain, and recommend better publicity and mobile vaccination camps, with a bibliography.