The essence of this chapter for last-minute revision: definitions, the sources-of-data classification, the key tables (population, literacy, iron ore index, frequency distribution), and the exclusive/inclusive and Ogive methods. The full notes, with the complete explanation, are available separately.
1 Six definitions to learn
Data are numbers that represent measurements from the real world. A Datum is a single measurement. Information is a meaningful answer to a query, or a meaningful stimulus that can cascade into further queries.
Primary sources are data collected for the first time by an individual, group or institution. Secondary sources are data collected from any published or unpublished record prepared earlier by someone else.
A Statistical Table is a systematic arrangement of data in columns and rows, meant to simplify presentation, facilitate comparison, and let a reader locate information quickly.
An Index Number is a statistical measure showing change in a variable with respect to time, place or other characteristics. Simple aggregate method: (Σq1 ÷ Σq0) × 100; the base year value is generally taken as 100.
Exclusive method: classes written as 20-30, 30-40, with the shared number excluded from the class where it is the upper limit. Inclusive method: classes written as 0-9, 10-19, with both limits included in the same class. Both methods span ten units per class.
An Ogive is the curve obtained by plotting cumulative frequencies. The “less than” method (starts at upper limits) gives a rising curve, the “more than” method (starts at lower limits) gives a declining curve.
2 Sources of data
| Primary sources (4 methods) | Key feature |
|---|---|
| Personal Observation | Direct field observation; needs theoretical knowledge + scientific attitude |
| Interview | Direct dialogue with respondent; 8 precautions listed |
| Questionnaire | Filled by the respondent themselves; only literate people; can be mailed |
| Schedule | Filled by a trained enumerator; works for illiterate respondents too |
| Secondary sources | Examples named in the chapter |
|---|---|
| Published: Government | Census of India, National Sample Survey, IMD Weather Reports, State Statistical Abstracts, Commission reports |
| Published: Quasi-government | Urban Development Authorities, Municipal Corporations, Zila Parishads |
| Published: International | UNESCO, UNDP, WHO, FAO; Demographic Year Book, Statistical Year Book, Human Development Report |
| Published: Private / Newspapers / Electronic media | Newspapers’ and private organisations’ yearbooks and surveys; the internet |
| Unpublished: Government Documents | Village-level revenue records maintained by the patwari |
| Unpublished: Quasi-government / Private | Municipal Corporation / District Council reports; companies’ and trade unions’ records |
Questionnaire vs Schedule is the single most-asked distinction in this chapter: a questionnaire is filled by the respondent themselves (so only literate people can be reached); a schedule is filled by a trained enumerator asking the questions (so illiterate respondents can be reached too).
3 Data compilation: three forms, with the book’s own tables
| Form | Meaning | Chapter’s table |
|---|---|---|
| Absolute Data | Original integers (raw data) | Table 1.1: Population of India, 2011 |
| Percentage / Ratio | Computed from a common parameter | Table 1.2: Literacy Rate, 1951-2011 |
| Index Number | Change relative to a base (=100) | Table 1.3: Iron ore production index |
- India’s population, 2011 (Table 1.1): 1,21,05,69,573 (Persons); 62,31,21,843 (Males); 58,74,47,730 (Females); Census 2011
- Literacy Rate formula: (Total Literates ÷ Total Population) × 100. India, 2011: 73.0% (Persons), 80.9% (Male), 64.6% (Female); 1951: 18.33% (Persons)
- Iron ore production index (Table 1.3, base year 1970-71 = 100): 1970-71 (32.5 mt) = 100; 1980-81 (42.2 mt) = 130; 1990-91 (53.7 mt) = 165; 2000-01 (67.4 mt) = 207
- New Delhi to Mumbai distance example: via Kota-Vadodara 1,385 km; via Itarsi-Manmad 1,542 km
4 Grouping raw data into a frequency distribution
| Group (exclusive method) | f | Cf |
|---|---|---|
| 0-10 | 4 | 4 |
| 10-20 | 5 | 9 |
| 20-30 | 5 | 14 |
| 30-40 | 7 | 21 |
| 40-50 | 6 | 27 |
| 50-60 | 10 | 37 |
| 60-70 | 8 | 45 |
| 70-80 | 6 | 51 |
| 80-90 | 5 | 56 |
| 90-100 | 4 | 60 |
“27 individuals score less than 50” and “45 out of 60 individuals lie below the score of 70”: both read directly off the Cf column above.
- Four and Cross Method = tally marks, used to count each observation into its class (Table 1.5)
- Exclusive method: 20-30, 30-40; shared number excluded from the “upper limit” class (Table 1.6)
- Inclusive method: 0-9, 10-19; both limits included in the same class (Table 1.7)
- Frequency Polygon: graph of a frequency distribution, drawn with a bar diagram + line graph together (Fig. 1.5)
- Ogive, “less than”: starts at upper limits, rising curve (Table 1.8, Fig. 1.6)
- Ogive, “more than”: starts at lower limits, declining curve (Table 1.9, Fig. 1.7)
- Both Ogives combined in one figure give a comparative picture (Table 1.10, Fig. 1.8)
Do not swap the two Ogive curves: the “less than” method gives a rising curve; the “more than” method gives a declining curve. And “both ends included” is the inclusive method, not the exclusive one.
- Data = measurements from the real world; Datum = one measurement; Information = a processed, meaningful answer
- Sources: Primary (Personal Observation, Interview: 8 precautions, Questionnaire/Schedule, Other Methods) vs Secondary (Published: Government/Quasi-govt/International/Private/Newspapers/Electronic; Unpublished: Government/Quasi-govt/Private documents)
- Data forms: Absolute (Table 1.1), Percentage/Ratio (Table 1.2, literacy rate), Index Number (Table 1.3, iron ore, base=100)
- Table 1.4: 60 students, scores 02-96, grouped into 10 classes of interval 10 (Tables 1.5/1.6)
- Exclusive (20-30, 30-40) vs Inclusive (0-9, 10-19) methods; Frequency Polygon; Ogive (less than = rising, more than = declining)
- River-crossing story: depths 0.6/0.8/0.9/1.5 m, average 0.95 m, child’s height 1 m: “statistical fallacy”