Exam-useful questions from this chapter, grouped by marks, each with a full model answer. Try writing the answer yourself first, then check it against this one.
1 1-Mark Questions
Q. Define ‘datum’.
Answer: Datum is a single measurement from the real world; data are numbers that represent many such measurements.
Q. How does the chapter define ‘information’?
Answer: Information is either a meaningful answer to a query or a meaningful stimulus that can cascade into further queries.
Q. Name the two sources through which data are collected.
Answer: Primary sources and Secondary sources.
Q. What is a Statistical Table?
Answer: A Statistical Table is a systematic arrangement of data in columns and rows, meant to simplify presentation and facilitate comparison.
Q. What is the formula for calculating an index number by the simple aggregate method?
Answer: Index Number = (Σq₁ ÷ Σq₀) × 100, where Σq₁ is the total of the current year’s production and Σq₀ is the total of the base year’s production; the base year value is taken as 100.
Q. What is another name for the Four and Cross Method?
Answer: Tally marks.
Q. Which symbol denotes cumulative frequency, and what does it represent?
Answer: Cf; it is obtained by adding successive simple frequencies to the sum of all frequencies before it.
Q. What is an Ogive?
Answer: An Ogive is the curve obtained by plotting cumulative frequencies.
2 2-Mark Questions
Q. Differentiate between data and information.
Answer: Data are raw numbers representing real-world measurements (e.g. rainfall in cm) that, on their own, may be difficult to draw conclusions from. Information is what results once data are processed: a meaningful answer to a query, or a meaningful stimulus that leads to further queries.
Q. What is ‘raw data’, and why does it require processing?
Answer: Raw data (also called absolute data) is data in its original, unprocessed form, appearing as a big jumble of numbers with the least comprehension, for example the ungrouped scores of 60 students in Table 1.4. It requires tabulation and classification (processing) so that meaningful inferences can be drawn and it becomes usable.
Q. Distinguish between a questionnaire and a schedule.
Answer: A questionnaire is filled up by the respondent themselves and is limited to literate, educated people; it can even be mailed to far-flung places. A schedule contains the same kind of questions, but a properly trained enumerator fills it up by asking the respondent, so it can also collect information from illiterate respondents.
Q. What is Personal Observation as a source of primary data?
Answer: Personal Observation is the collection of information by an individual or a group through direct observation in the field, for example a field survey collecting data on relief, drainage, soil, natural vegetation or population characteristics. It requires the observer to have theoretical knowledge of the subject and a scientific attitude for unbiased evaluation.
Q. List any four published sources of secondary data mentioned in the chapter.
Answer: Any four of: Government Publications (e.g. Census of India), Semi/Quasi-government Publications, International Publications (UN agencies), Private Publications, Newspapers and Magazines, Electronic Media.
Q. List the three unpublished sources of secondary data given in the chapter.
Answer: Government Documents (e.g. village-level revenue records kept by the patwari), Quasi-government Records (e.g. Municipal Corporation/District Council reports), and Private Documents (e.g. records of companies, trade unions and organisations).
Q. What is the exclusive method of forming class intervals?
Answer: In the exclusive method, the upper limit of one class is the same number as the lower limit of the next class (e.g. 20-30, 30-40); a value equal to that shared number is included in the class where it is the lower limit and excluded from the class where it is the upper limit; hence the name ‘exclusive’.
Q. What is the inclusive method of forming class intervals?
Answer: In the inclusive method, both the upper and lower limits of a class are included within that class (e.g. 0-9, 10-19); the upper limit of a class normally differs from the lower limit of the next by 1, and each class still spans ten units.
Q. Distinguish between simple frequency and cumulative frequency.
Answer: Simple frequency (f) is the number of individuals falling in each class; the sum of all simple frequencies equals N (Σf = N). Cumulative frequency (Cf) is obtained by adding each simple frequency successively to the sum of all the frequencies before it, so the last cumulative frequency also equals N.
Q. What is a Frequency Polygon, and how is it drawn?
Answer: A Frequency Polygon is a graph of a frequency distribution, used to compare two or more frequency distributions; it is drawn by showing the two frequencies together using a bar diagram and a line graph.
Q. Explain the ‘less than’ method of constructing an Ogive.
Answer: In the less than method, plotting starts with the upper limit of each class, and the frequencies are added on successively; when these cumulative frequencies are plotted, a rising curve is obtained (Table 1.8, Fig. 1.6).
3 4-Mark Questions
Q. Explain the four sources of primary data, with one example of each, as given in the chapter.
Answer: 1) Personal Observation: direct field observation of relief, drainage, soil or population features, requiring theoretical knowledge and a scientific attitude.
2) Interview: direct dialogue and conversation between the researcher and the respondent, following eight stated precautions (e.g. taking the respondent into confidence, using simple and polite language).
3) Questionnaire/Schedule: a set of written questions; a questionnaire is filled by the respondent themselves (limited to literate people), while a schedule is filled by a trained enumerator who asks the questions.
4) Other Methods: direct field measurement using instruments, e.g. a soil kit or water quality kit, or transducers used by field scientists to assess crop and vegetation health.
Q. Describe, with the chapter’s own example, how an index number is calculated using the simple aggregate method.
Answer: An index number shows change in a variable over time, location or other characteristics, using the formula (Σq₁ ÷ Σq₀) × 100, with the base year value taken as 100.
Worked example (Table 1.3, iron ore production, base year 1970-71):
1970-71: 32.5 million tonnes = index 100 (base year)
1980-81: 42.2 million tonnes, so (42.2÷32.5)×100 = index 130
1990-91: 53.7 million tonnes, so (53.7÷32.5)×100 = index 165
2000-01: 67.4 million tonnes, so (67.4÷32.5)×100 = index 207
The rising index numbers show iron ore production more than doubling between 1970-71 and 2000-01.
Q. Explain the steps involved in classifying raw data into a grouped frequency distribution, using the chapter’s own example (Table 1.4).
Answer: 1) Find the range of the raw data: Table 1.4’s scores of 60 students range from 02 to 96.
2) Decide the number of classes and the class interval: conveniently chosen as ten classes of interval ten (0-10, 10-20, … 90-100).
3) Classify each observation into its class using the Four and Cross Method (tally marks); shown in Table 1.5.
4) Count the tally marks in each class to get the simple frequency (f), and add these successively to get the cumulative frequency (Cf); shown in Table 1.6, with Σf = N = 60.
Q. Distinguish between the exclusive and inclusive methods of classification, with the chapter’s own examples.
Answer: Exclusive method (Table 1.6): classes are written as 20-30, 30-40, etc.; the upper limit of one class equals the lower limit of the next, so a value equal to that shared number is placed in the class where it is the lower limit and excluded from the class where it is the upper limit.
Inclusive method (Table 1.7): classes are written as 0-9, 10-19, etc.; both the upper and lower limits of a class are included in that same class, and the upper limit of a class normally differs from the lower limit of the next class by 1.
Common point: each class spans ten units in both methods.
Q. Explain the ‘more than’ method of constructing an Ogive, and how it differs from the ‘less than’ method.
Answer: In the ‘more than’ method, plotting starts with the lower limit of each class, and the cumulative frequency is obtained by subtracting the class’s own frequency from the running cumulative total; when these are plotted, a declining curve is obtained (Table 1.9, Fig. 1.7).
This differs from the ‘less than’ method, which starts at the upper limits of classes and adds frequencies on successively, producing a rising curve (Table 1.8, Fig. 1.6).
The two curves can be combined in one figure (Table 1.10, Fig. 1.8) to give a comparative picture, and they cross at a point common to both series.
Q. What precautions should be taken while conducting an interview, according to the chapter?
Answer: 1) Prepare a precise list of items about which information is to be gathered.
2) Be clear about the objective of the survey.
3) Take the respondent into confidence before asking any sensitive question, and assure secrecy.
4) Create a congenial atmosphere so the respondent explains facts without hesitation.
5) Use simple, polite language so the respondent feels motivated to answer.
6) Avoid questions that may hurt the respondent’s self-respect or religious feelings.
7) At the end, ask if the respondent can provide any additional information.
8) Thank the respondent for sparing their time.
4 6-Mark Questions
Q. “Data are of no use unless they are collected, tabulated, classified and presented systematically.” Discuss this statement with reference to the sources of data and their compilation, as described in the chapter.
Answer: Collection: Data are first collected from Primary Sources (Personal Observation, Interview, Questionnaire/Schedule, and Other Methods such as soil/water testing kits and transducers) or Secondary Sources (published records like Government/International/Private Publications and newspapers, or unpublished records like Government Documents, Quasi-government Records and Private Documents).
Why raw collection is not enough: Data collected this way first appear as a jumble of information called raw data, with the least comprehension. As the chapter’s own river-crossing story shows, even a correctly calculated figure (an average depth of 0.95 m) can hide a dangerous fact (one point 1.5 m deep) if it is not examined carefully. This is called statistical fallacy.
Tabulation and classification: Raw data is turned into a Statistical Table, a systematic arrangement in columns and rows, to simplify presentation, facilitate comparison, and let information be located quickly. Table 1.4’s 60 raw scores, for instance, are classified into ten classes of interval ten (Table 1.5, 1.6) using the Four and Cross Method.
Presentation: Once classified, data are presented as absolute data (Table 1.1), percentages/ratios such as literacy rate (Table 1.2), or index numbers (Table 1.3), and further displayed graphically as a Frequency Polygon or an Ogive.
Conclusion: Only after this full sequence (collection, tabulation, classification and systematic presentation) does raw data become usable information from which valid conclusions can be drawn; skipping any step, as the river-crossing story shows, can lead to a seriously wrong conclusion.
Q. Explain the concept of a frequency distribution. Using Table 1.6, describe how simple frequency, cumulative frequency, the exclusive method and the inclusive method are all related to the same grouped data set.
Answer: Frequency distribution: A table showing how the different values of a variable are distributed across classes, obtained after grouping raw data (Table 1.4, scores 02 to 96 of 60 students) into classes of a chosen interval.
Simple frequency (f): the number of individuals in each class, found using the Four and Cross Method / tally marks (Table 1.5); Σf = N = 60.
Cumulative frequency (Cf): obtained by adding each class’s simple frequency successively to the sum of all preceding frequencies (Table 1.6); e.g. Cf for 40-50 is 27, meaning 27 individuals scored less than 50; the last Cf (60) again equals N.
Exclusive method: Table 1.6 itself uses this method; classes are written as 0-10, 10-20, etc., with the upper limit of one class equal to the lower limit of the next, and a value at that shared point excluded from the class where it is the upper limit.
Inclusive method: the same underlying data can instead be classified with Table 1.7’s classes (0-9, 10-19, etc.), where both limits of a class are included in it; the f and Cf values in Table 1.7 are identical to Table 1.6’s, since it is the same 60 scores, only the class-writing convention differs.
Together, these four ideas describe one continuous process: the same 60 raw scores are grouped, classified by one of the two conventions, counted as simple frequencies, and then accumulated as cumulative frequencies; this is the basis for drawing the Frequency Polygon and the Ogive.
5 Case Studies
(A) 1 mark What was the average depth of the river, as calculated in the passage?
Answer: 0.95 metres.
(B) 1 mark What was the height of the child in the passage?
Answer: 1 metre.
(C) 2 marks Based on the passage, name the statistical concept this incident illustrates, and explain why the average depth misled the person.
Answer: The incident illustrates ‘statistical fallacy’. Although the average of the four measured depths (0.6, 0.8, 0.9 and 1.5 m) was 0.95 m, less than the child’s height of 1 m, one of those four points was actually 1.5 m deep, well above the child’s height, and it was at that point that the child drowned; the single average figure hid this fact.
(A) 1 mark According to the passage, what two categories make up secondary sources of data?
Answer: Published and unpublished records.
(B) 1 mark Who maintains the village-level revenue records mentioned in the passage?
Answer: The patwari of the respective village.
(C) 2 marks Based on the passage, explain why village-level revenue records count as an unpublished secondary source.
Answer: They are prepared and maintained as records at the village level of governance by the patwari and are never brought out as a printed publication, unlike a government publication such as the Census of India; because they were compiled earlier by an authority other than the present investigator and remain available to be consulted, they still count as a secondary source: an unpublished one.