Data Interpretation — Sources, Representation & Analysis

Data are raw, unorganised facts and figures; once they are processed and given meaning they become information; organised information that guides action becomes knowledge. The examiner loves this ladder — Data → Information → Knowledge → Wisdom (the DIKW hierarchy) — because it explains why collecting numbers is not the same as understanding them.

Acquisition is how the numbers reach you. Data may be collected by a census (every unit of the population is enumerated) or by a sample survey (a representative part is studied and the result is generalised). The common instruments are observation, interview, questionnaire (filled by the respondent), schedule (filled by the investigator), experiment, and administrative or registration records. Increasingly there is a fourth channel: machine-generated data from sensors, transactions, mobile phones and web logs — the raw material of big data.

Once acquired, data must be classified — put into homogeneous groups. The four standard bases are: geographical (by place, also called spatial), chronological (by time, giving a time series), qualitative (by an attribute such as sex or medium of instruction — simple if one attribute, manifold if several), and quantitative (by a measurable variable such as marks or income, giving a frequency distribution). A quantitative series can be individual (each value listed), discrete (values with frequencies), or continuous (class intervals with frequencies).

• Tabulation follows classification: a good table has a title, stub (row headings), caption (column headings), body, unit statement, head-note and foot-note/source. NET has asked for these parts by name.
• Editing of collected data means checking for completeness, consistency, accuracy and homogeneity before analysis; coding converts answers into symbols/numbers for processing.
• Cross-sectional data describe many units at one point of time; time-series data describe one unit over many time points; panel (longitudinal) data follow the same units across time — the strongest of the three for studying change.

Quantitative data answer how much / how many and are numerical. They split into discrete (countable, whole values only — number of students in a class) and continuous (measurable, any value in a range — height, time, temperature). Qualitative (categorical) data answer what kind and describe an attribute — gender, religion, medium of instruction, satisfaction level. Qualitative data can still be counted (frequency of each category) but they cannot be meaningfully averaged.

A diagram is not decoration; it is a compression device. It trades precision for instant comparison. The examiner therefore asks a very specific kind of question: given this type of data, which diagram is appropriate? Learn the table below as a matching exercise, because that is exactly how it is tested.

Mapping of data (cartographic representation) is the geographical branch of the same skill: instead of an axis, the space itself carries the number. It matters for governance because policy is delivered district by district.

Two numbers summarise any dataset: a measure of central tendency (where the middle is) and a measure of dispersion (how spread out the values are). NET does not want proofs — it wants you to compute quickly and to know which measure is safe to use.

1. Arithmetic mean = Σx ÷ n. Uses every value, so it is the most efficient — but a single extreme value drags it.
2. Median = the middle value after arranging in order. For odd n it is the ((n+1)/2)-th value; for even n it is the average of the two middle values. Unaffected by extremes — the right choice for income, land holding and any ordinal data.
3. Mode = the most frequently occurring value. The only average available for nominal data. A set may have no mode, one mode, or two (bimodal).
4. Range = maximum − minimum. The crudest dispersion measure, decided entirely by the two most unusual values.
5. Standard deviation (σ) = the square root of the average of squared deviations from the mean. Its square is the variance. The coefficient of variation = (σ ÷ mean) × 100 lets you compare the consistency of two groups measured in different units.

Work through one small dataset completely. Take the eight marks: 2, 4, 4, 4, 5, 5, 7, 9 (already in ascending order).

Read the pattern: mode 4 < median 4.5 < mean 5. When the mean is pulled to the right of the median, the distribution is positively (right) skewed — a few high values (here 7 and 9) are stretching the tail. Note also that dividing Σ(x − mean)² by n gives the population standard deviation (2 exactly); dividing by n − 1 = 7 gives the sample standard deviation, √(32 ÷ 7) ≈ 2.14. Both are correct — the question must tell you which.

The table below would appear in the exam as a multiple bar chart (two bars per year) or as two line graphs. Written as a table, nothing is lost. The figures are illustrative and invented for practice — they are not official statistics. The last two columns were not given; we computed them, and that is the whole job.

1. Growth rate. Formula: (New − Old) ÷ Old × 100. For 2020: (2,400 − 2,000) ÷ 2,000 × 100 = 400 ÷ 2,000 × 100 = 20%. For 2021: 300 ÷ 2,400 × 100 = 12.5%. For 2022: 540 ÷ 2,700 × 100 = 20%. For 2023: 324 ÷ 3,240 × 100 = 10%.
2. Absolute versus percentage — the trap in action. The rises of 2020 and 2022 are both exactly 20%, yet in heads they are very different: +400 students in 2020 against +540 in 2022. Equal percentage, unequal number, because the base grew from 2,000 to 2,700. Conversely the largest absolute rise (+540 in 2022) is not the largest percentage rise — it merely ties for it.
3. Total growth over the period. 2019 → 2023: (3,564 − 2,000) ÷ 2,000 × 100 = 1,564 ÷ 2,000 × 100 = 78.2%. Never add the yearly rates (20 + 12.5 + 20 + 10 = 62.5%) — that ignores compounding and is wrong.
4. Female enrolment grew faster. 800 → 1,782 is a rise of 982, i.e. 982 ÷ 800 × 100 = 122.75%, against 78.2% for the total. Whenever a part grows faster than the whole, the part’s share must rise — and indeed the share went from 40.0% to 50.0%.
5. Share can fall while the number rises — 2022 proves it. Female enrolment rose from 1,296 to 1,458, a healthy 162 ÷ 1,296 × 100 = 12.5% increase. Yet the female share fell from 48.0% to 45.0%, because the total grew faster (20%). Growing slower than the whole means losing share even while growing.
6. Ratio. In 2019 female : male = 800 : (2,000 − 800) = 800 : 1,200 = 2 : 3. In 2023 female : male = 1,782 : (3,564 − 1,782) = 1,782 : 1,782 = 1 : 1 — perfect parity.
7. Averages of the series. Mean annual enrolment = 13,904 ÷ 5 = 2,780.8. Median of 2,000 / 2,400 / 2,700 / 3,240 / 3,564 = the third value = 2,700. There is no mode (every value occurs once). Range = 3,564 − 2,000 = 1,564. Overall female share = 6,416 ÷ 13,904 × 100 = 46.1% (to one decimal).

A pie chart carries exactly three linked columns — share, central angle and amount. Fill any one and the other two follow, because 1% = 3.6° and amount = share × total. The figures below are illustrative, invented for practice.

1. Angle from share. 1% = 360 ÷ 100 = 3.6°. School education 40% × 3.6 = 144°; higher education 25% × 3.6 = 90° (a right angle — always a quarter); research 15% × 3.6 = 54°; skill 12% × 3.6 = 43.2°; administration 8% × 3.6 = 28.8°. Check the column: 144 + 90 + 54 + 43.2 + 28.8 = 360°. If your angles do not total 360°, you have made an error — this self-check costs five seconds and saves a mark.
2. Amount from angle — the per-degree shortcut. ₹9,000 crore ÷ 360° = ₹25 crore per degree. So research at 54° = 54 × 25 = ₹1,350 crore, and skill development at 43.2° = 43.2 × 25 = ₹1,080 crore. Column check: 3,600 + 2,250 + 1,350 + 1,080 + 720 = ₹9,000 crore.
3. Ratios read straight off the share column. Higher education : research = 25 : 15 = 5 : 3 (confirm with the money: 2,250 : 1,350 = 5 : 3). School education is 40 ÷ 8 = 5 times administration (3,600 ÷ 720 = 5). And higher education + research = 25 + 15 = 40% = ₹3,600 crore — exactly equal to school education. Because both columns are proportional to the shares, you can answer ratio questions without touching the rupee figures at all.
4. Percentage-point versus per cent. If next year higher education moves from 25% to 30%, that is a rise of 5 percentage points, but a rise of 5 ÷ 25 × 100 = 20 per cent. NET has asked this distinction directly; never use the two words as synonyms.

Now the stem-and-leaf display, the one diagram that is fully printable. Fifteen scores were recorded: 23, 25, 27, 31, 34, 36, 38, 42, 45, 47, 47, 49, 52, 56, 61. Split each number into a stem (tens digit) and a leaf (units digit).

• The shape is visible at a glance: the longest row is stem 4, so the data pile up in the forties. Frequencies 3, 4, 5, 2, 1 total 15 — always verify against n.
• Median. n = 15 is odd, so the median is the (15 + 1) ÷ 2 = 8th value. The cumulative column says 7 values lie below stem 4, so the 8th value is the first leaf of stem 4, namely 42.
• Mode and range. Only 47 repeats (leaf 7 twice on stem 4), so mode = 47. Range = 61 − 23 = 38. Notice that a histogram would have destroyed this information; the stem-and-leaf keeps every original value.

This is the dataset from which the exam draws a histogram, a frequency polygon and an ogive — all three from one table. Marks of 200 students in a test (illustrative, invented for practice):

1. Reading the cumulative column directly. Students scoring below 40 = 86, i.e. 86 ÷ 200 × 100 = 43%. Students scoring 50 or more = 38 + 22 = 60, i.e. 60 ÷ 200 × 100 = 30% — equivalently 200 − 140 = 60. Students in the range 30–50 = 46 + 54 = 100, exactly half the class.
2. Mean of grouped data = Σ(f × mid-point) ÷ Σf = 8,440 ÷ 200 = 42.2 marks. Verify the numerator: 180 + 700 + 1,610 + 2,430 + 2,090 + 1,430 = 8,440.
3. Median class and median. N ÷ 2 = 100. Scan the cumulative column: 86 is below 100, 140 is above it, so the 100th student sits in the class 40–50 — that is the median class. Then median = L + [(N/2 − cf) ÷ f] × h = 40 + [(100 − 86) ÷ 54] × 10 = 40 + (14 ÷ 54) × 10 = 40 + 2.59 = 42.59 marks.
4. Modal class and mode. The highest frequency is 54, so the modal class is 40–50. Mode = L + [(f₁ − f₀) ÷ (2f₁ − f₀ − f₂)] × h = 40 + [(54 − 46) ÷ (108 − 46 − 38)] × 10 = 40 + (8 ÷ 24) × 10 = 40 + 3.33 = 43.33 marks.
5. Cross-check with the empirical relation. Mode ≈ 3 × Median − 2 × Mean = 3 × 42.59 − 2 × 42.2 = 127.77 − 84.40 = 43.37, which is very close to the computed 43.33. Since mean 42.2 < median 42.59 < mode 43.33, the distribution is mildly negatively (left) skewed.
6. What each diagram would show. A histogram of this table has six touching rectangles, tallest over 40–50. A frequency polygon joins the six mid-points 15, 25, 35, 45, 55, 65. A "less than" ogive plots 12, 40, 86, 140, 178, 200 against the upper boundaries 20, 30, 40, 50, 60, 70; dropping a perpendicular from cumulative frequency 100 onto the X-axis reads off the median, ≈ 42.6.

Unit 7 ends where statistics meets the state: "data and governance". The idea is simple. A government that measures can target; a government that publishes can be held accountable; and a government that collects must protect. Evidence-based policy replaces guesswork with counting — which is why Aadhaar-linked Direct Benefit Transfer, real-time dashboards and geo-tagged asset registers changed Indian administration more than any single law.

• E-governance is the use of ICT to deliver public services, and its four interaction types are G2C (government to citizen), G2B (government to business), G2G (government to government) and G2E (government to employee). The promised gains are the SMART ones — Simple, Moral, Accountable, Responsive, Transparent governance.
• Big data is described by the five V’s — Volume (scale), Velocity (speed of arrival), Variety (text, image, sensor, log), Veracity (trustworthiness) and Value (usable insight). In administration it powers GST analytics, crop-yield estimation from satellite imagery, epidemic surveillance and traffic management.
• Open data must be more than merely published: the accepted tests are that it be machine-readable, in a non-proprietary format, complete, timely, and licensed for free reuse. A scanned PDF of a table is published but not open, because the numbers cannot be read by software.
• The costs are real too: the digital divide (access, affordability, digital literacy, language), exclusion errors when biometric authentication fails, surveillance risk, algorithmic bias inherited from skewed training data, and the danger of statistical opacity when methodology is not published alongside the number.