Unit 1: Statistics and data collection
Fundamental of Statistics notes · PTU syllabus (UGCC2504)
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Unit summary
Statistics is the science of collecting, organising, analysing and interpreting numerical data to make decisions. For a BCA student it is the base of data analysis, data science and machine learning.
This unit covers the meaning, scope, functions, uses and limitations of statistics, the methods of collecting primary and secondary data, statistical errors, and rounding off data.
After this unit you can
- Define statistics in both the singular and plural sense
- Explain the functions, scope, importance and limitations of statistics
- Compare primary and secondary data and their collection methods
- Identify statistical errors and round off data correctly
PTU syllabus topics
- Origin
- features
- scope
- functions
- uses
- importance and limitations of statistics
- primary and secondary data collection methods
- statistical errors
- rounding off data
Source
Collected first-hand for this study
Already collected by someone else
Examples
Survey, interview, observation
Census, reports, published records
Cost and time
Higher
Lower
Reliability
Fits your purpose exactly
May not match your needs
Topic 1
Meaning and origin of statistics
The word statistics comes from the Latin status and Italian statista, because it began as the collection of data by states — population, land and taxes.
- Plural sense: statistics are numerical facts, such as the marks of students or the monthly sales of a shop.
- Singular sense: statistics is the science of collecting, classifying, presenting, analysing and interpreting data.
Horace Secrist defined statistics (plural) as "aggregates of facts affected to a marked extent by a 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."
Topic 2
Features, functions and scope
Features of statistics (from Secrist's definition): they are aggregates of facts, numerically expressed, affected by many causes, collected systematically for a predetermined purpose, estimated with reasonable accuracy and comparable.
- 1Collection
Gather data
- 2Organisation
Edit and classify
- 3Presentation
Tables, diagrams, graphs
- 4Analysis
Averages, dispersion, correlation
- 5Interpretation
Draw conclusions
Functions: it simplifies complex data, compares facts, helps in forecasting, tests hypotheses, helps policy-making and enlarges individual knowledge. Scope and uses: business (demand forecasting, quality control), economics (national income, inflation), government (census, planning), IT (data analysis, machine learning, A/B testing), medicine (clinical trials) and research.
Topic 3
Importance and limitations
Data
Turns raw data into useful information
Studies only numerical (quantitative) data
Groups
Summarises large groups
Does not study individuals
Results
Supports decisions and forecasts
Results are true only on average
Use
Universal across fields
Can be misused by people with bias
Exam tip
The famous saying "Statistics can prove anything" reflects misuse, not a fault of statistics itself. Mention this when discussing limitations.
Topic 4
Primary and secondary data
- Primary data is collected for the first time by the investigator for a specific purpose. It is original and reliable, but costly and time-consuming.
- Secondary data has already been collected by someone else (government reports, RBI publications, company records, websites). It is quick and cheap, but may not exactly fit the purpose.
| Primary data methods | Secondary data sources |
|---|---|
| Direct personal investigation | Government publications (Census, NSSO) |
| Indirect oral investigation | Reports of committees and commissions |
| Information through local correspondents | Journals, newspapers, research papers |
| Questionnaires filled by informants | Company and trade association records |
| Schedules filled by enumerators | Websites and online databases |
Exam tip
Before using secondary data, check its reliability, suitability and adequacy — this is a standard exam point.
Topic 5
Statistical errors and rounding off
A statistical error is the difference between the true value and the estimated or approximated value. It does not mean a mistake.
- Biased errors build up in one direction (for example a faulty weighing machine).
- Unbiased (compensating) errors occur randomly in both directions and tend to cancel out.
- Absolute error = true value − estimated value; relative error = absolute error / estimated value.
Rounding off expresses a figure to a convenient approximation: to the nearest whole number, ten, hundred or decimal place. If the digit dropped is 5 or more, the last retained digit is increased by one.
Example
4,567 rounded to the nearest hundred is 4,600; 3.146 rounded to two decimal places is 3.15.
Key terms
- Statistics (plural)
- Numerical facts collected systematically
- Statistics (singular)
- The science of collecting, analysing and interpreting data
- Primary data
- Original data collected first-hand for a purpose
- Secondary data
- Data already collected by someone else
- Statistical error
- The difference between a true and an estimated value
Quick revision
- Stages: collection, organisation, presentation, analysis, interpretation.
- Statistics deals with aggregates and numbers, not individuals.
- Primary = original but costly; secondary = cheap but must be checked.
- Biased errors accumulate; unbiased errors cancel out.
Important exam questions
Practice questions written to the PTU exam pattern for this unit's syllabus: short answers (Section A style) and long answers (Sections B and C style).
Short-answer questions
- Q1.Define statistics in the singular and plural sense.
- Q2.List four limitations of statistics.
- Q3.Differentiate between primary and secondary data.
- Q4.What is a questionnaire?
- Q5.Differentiate between biased and unbiased errors.
- Q6.Round 12.4567 to two decimal places.
Long-answer questions
- Q1.Explain the meaning, features, functions and scope of statistics.
- Q2.Discuss the importance and limitations of statistics.
- Q3.Explain the various methods of collecting primary data with their merits and demerits.
- Q4.What precautions should be taken while using secondary data?
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