Topics Covered
Sources of Data
Classification of Data
Quantitative and Qualitative Data
Scales of Measurement
Bar Charts and Histograms
Pie Charts
Line Charts
Reading a Table
Data and Governance
Contents
Topic Overview — What & Why
Unit VII is the statistics unit of Paper I. Its questions come in two kinds: concepts (primary or secondary data, which scale a variable is on, which chart suits which data, how India governs its data) and data sets, usually a table or chart followed by five questions of arithmetic: totals, percentages, growth rates, ratios and averages. The arithmetic is that of Unit V; the skill is to read the table correctly and compute only what is asked.
- Sources: primary (collected for the purpose) and secondary (collected by someone else); by census or by sample.
- Kinds: quantitative (discrete or continuous) and qualitative; nominal, ordinal, interval and ratio scales.
- Charts: a bar chart for categories, a histogram for a continuous variable, a pie chart for shares of a whole, a line chart for change over time.
- Governance: open government data, the data-sharing policy of 2012, data.gov.in, and the Digital Personal Data Protection Act, 2023.
1. Sources, Acquisition and Classification of Data
| Primary data | Secondary data | |
|---|---|---|
| Collected by | The investigator, for the present purpose | Someone else, for another purpose |
| Methods or sources | Direct interview, questionnaire, schedule, observation, experiment | Published reports, census tables, surveys of government agencies, journals, administrative records, online databases |
| Strengths | Fits the purpose; the method is known | Cheap and quick; often large |
| Weakness | Costly and slow | May not fit the purpose; definitions and accuracy must be checked |
- A questionnaire is filled in by the respondent; a schedule is filled in by the enumerator who asks the questions.
- A census covers every unit of the population; a sample survey covers a part chosen to represent it. India's population census is taken under the Census Act, 1948; national sample surveys are run by the National Statistics Office of the Ministry of Statistics and Programme Implementation.
- Classification arranges data into groups by a common character. It is geographical (by place), chronological (by time), qualitative (by attribute, such as sex or religion) or quantitative (by size, such as income classes). Tabulation sets the classified data out in rows and columns.
EXAMPLE 1
A researcher interviews 200 farmers about crop insurance: primary data. She also uses the state's published crop-yield tables: secondary data.
EXAMPLE 2
A table of students by state of origin is a geographical classification; a table of enrolment for each year from 2015 to 2025 is chronological.
2. Quantitative and Qualitative Data
- Quantitative data are numbers that measure or count. They are discrete (counts that take separate values: number of children) or continuous (measurements that can take any value in a range: height, time).
- Qualitative (categorical) data record a quality or category: blood group, opinion, mother tongue.
The scales of measurement, set out by S. S. Stevens in 1946:
| Scale | What it allows | Example | Central value |
|---|---|---|---|
| Nominal | Names and categories, no order | Blood group, roll number | Mode |
| Ordinal | Order, but differences not equal | Rank in class, grade A/B/C, Likert ratings | Median |
| Interval | Equal differences, no true zero | Temperature in °C, calendar year | Mean |
| Ratio | Equal differences and a true zero, so ratios make sense | Height, income, marks | Mean (geometric mean too) |
EXAMPLE 1
"40 °C is twice as hot as 20 °C" is wrong: Celsius is an interval scale, whose zero is not an absence of heat. "₹40,000 is twice ₹20,000" is right: income is on a ratio scale.
EXAMPLE 2
Responses "strongly disagree" to "strongly agree" are ordinal; their median is meaningful, their mean is at best a convention.
3. Graphical Representation and Mapping of Data
| Chart | Use it for | Note |
|---|---|---|
| Bar chart | Comparing categories | Bars separate, of equal width; only the height matters. Grouped (multiple) and stacked (component) forms compare parts |
| Histogram | The distribution of a continuous variable | Bars touch; the area of each bar is the frequency, so unequal classes need adjusted heights |
| Frequency polygon, ogive | The shape of a distribution; cumulative frequency | The ogive locates the median and quartiles |
| Pie chart | Shares of one whole | A share of p% takes p × 3.6 degrees; 25% is 90° |
| Table chart | Exact values | Rows, columns, totals and a stated unit |
| Line chart | Change over time | The slope shows the rate of change |
Mapping of data shows values by place. A choropleth map shades each area by its value (literacy by district); a dot map places one dot for a fixed number of cases; a proportional symbol map sizes a circle by the value. Geographic information systems (GIS) combine such maps in layers.
EXAMPLE 1
A college spends ₹12 lakh of a ₹48 lakh budget on the library. On a pie chart the library's sector is 12/48 × 360° = 90°.
EXAMPLE 2
Monthly rainfall over a year is best shown as a line or bar chart by month; the distribution of students' heights, as a histogram.
4. Data Interpretation
Read the title, the unit (thousands? lakhs? percent?) and the column headings before any question. Then compute only what is asked, and estimate first to rule out options.
- Percentage share = part ÷ total × 100.
- Percentage growth from one year to the next = (this year − last year) ÷ last year × 100.
- Ratio: reduce to lowest terms.
- Average over years = total ÷ number of years.
- A percentage of a percentage is a product: 40% of 25% is 10%.
EXAMPLE
Enrolment (in thousands) in three colleges:
| College | 2023 | 2024 | 2025 |
|---|---|---|---|
| P | 40 | 45 | 54 |
| Q | 60 | 63 | 66 |
| R | 50 | 42 | 60 |
- Total enrolment in 2025: 54 + 66 + 60 = 180 thousand.
- P's growth from 2024 to 2025: (54 − 45) ÷ 45 × 100 = 20%.
- R's share of the 2024 total: 42 ÷ (45 + 63 + 42) × 100 = 42 ÷ 150 × 100 = 28%.
- Q's average over the three years: (60 + 63 + 66) ÷ 3 = 63 thousand.
- Ratio of P to R in 2023: 40 : 50 = 4 : 5.
5. Data and Governance
- The National Data Sharing and Accessibility Policy (NDSAP), notified in 2012, provides for non-sensitive data held by government bodies to be shared openly, in machine-readable form.
- data.gov.in, the Open Government Data Platform India, run by the National Informatics Centre, publishes those datasets.
- The Collection of Statistics Act, 2008 governs the collection of statistics by government and protects the confidentiality of the information given.
- The Digital Personal Data Protection Act, 2023 governs the processing of digital personal data: consent, the duties of data fiduciaries, the rights of data principals, and a Data Protection Board.
- Data in delivering services: Aadhaar identity, under the Aadhaar Act, 2016, and Direct Benefit Transfer, which pays subsidies and benefits straight into beneficiaries' bank accounts, are examples of governance that runs on data; the dashboards of government schemes publish their progress.
- Good data governance means quality (accurate, timely, consistent), access (open where it can be), privacy and security (protected where it must be) and accountability (who is responsible for each dataset).
EXAMPLE 1
A researcher wants district-wise rainfall data released by a government department. data.gov.in is the first place to look, under the NDSAP.
EXAMPLE 2
A survey office publishes district averages but not any household's answers. That is the confidentiality the Collection of Statistics Act, 2008 requires.
Exam pointers for Unit VII.
- Primary: collected by you, for this purpose. Secondary: by others, for theirs.
- Questionnaire: the respondent fills it in. Schedule: the enumerator does.
- Nominal → mode; ordinal → median; interval and ratio → mean. Only a ratio scale has a true zero.
- Bar chart for categories, histogram for a continuous variable (area = frequency), pie for shares (1% = 3.6°), line for time.
- Growth is on last year's value; a share is of the right total.
- NDSAP 2012; data.gov.in; the Collection of Statistics Act 2008; the DPDP Act 2023.
Final Revision Checklist
- Primary and secondary data, census and sample; questionnaire and schedule; the four classifications.
- Discrete, continuous and qualitative data; the four scales and their central values.
- Which chart for which data; pie-chart angles; maps of data.
- Totals, shares, growth rates, ratios and averages from a table.
- Open government data, the data-sharing policy, statistics law and data protection.
Sources
- National Data Sharing and Accessibility Policy, 2012, Gazette of India, and the Open Government Data Platform: data.gov.in.
- The Collection of Statistics Act, 2008; the Census Act, 1948: mospi.gov.in and censusindia.gov.in.
- The Digital Personal Data Protection Act, 2023: meity.gov.in.
- The Aadhaar (Targeted Delivery of Financial and Other Subsidies, Benefits and Services) Act, 2016: uidai.gov.in; Direct Benefit Transfer: dbtbharat.gov.in.
- S. S. Stevens, "On the Theory of Scales of Measurement", Science (1946).