Notes/Class 12/Review of Basic Subject Matter of Statistics
Class 12Unit 13 14 marksVery Short AnswerShort AnswerLong AnswerNumerical

Review of Basic Subject Matter of Statistics

Statistics is the science of numerical statements of facts that are capable of analysis and interpretation. In the plural sense, statistics means numerical facts (data) collected systematically for a predetermined purpose; in the singular sense, it is the science of methods and techniques of collection, presentation, analysis and interpretation of data. Statistics has four aspects — collection, organisation, analysis, and interpretation. It is widely used in economics, planning, business, state administration, natural science, social science and mathematics. Limitations: statistics does not study individuals, is not suitable for qualitative phenomena, its laws are not exact, and it can be misused.

Statistics — Meaning & Definition

  1. Plural sense — "statistics" means numerical facts and figures collected systematically for a predetermined purpose (e.g. Nepal's population 29.16 million in Census 2021; inflation 5.4% in 2023/24)
  2. Singular sense — "statistics" means the science of methods and techniques used to collect, present, analyse and interpret such data (e.g. calculating mean, median, mode, standard deviation). In Class 12 we study both senses — we use statistical methods to make sense of data collected by the Central Bureau of Statistics (CBS)

Statistics — Singular sense vs Plural sense

BasisSingular SensePlural Sense
MeaningScience of methods & techniquesNumerical facts & figures
NatureA method / toolData themselves
ExampleFormula of mean: Σx/nCensus 2021 population = 29.16 million
Question answeredHow to collect & analyse data?What does the data show?
Used byStatistician, researcherGovernment, CBS, business
FieldStatistics as a subjectStatistics as numerical data

Aspects of Statistics

  1. Collection of data — gathering raw data (e.g. CBS sends enumerators to every household in the National Census)
  2. Organisation / Presentation of data — arranging data into tables, frequency distributions, charts and graphs (e.g. bar chart of Nepal's population by province)
  3. Analysis of data — applying statistical tools such as mean, median, mode, standard deviation, correlation, index numbers (e.g. calculating the average household income from NLSS data)
  4. Interpretation of data — drawing conclusions and making decisions (e.g. interpreting that poverty fell from 25% to 18.7% means policy is working). The first two are descriptive; the last two are analytical

Characteristics of Statistics (Plural Sense)

  • Aggregate of facts — a single number (e.g. one person's height) is not statistics; many numbers (heights of all Class 12 students) are.
  • Numerically expressed — qualitative facts like "Nepalese are friendly" cannot be statistics unless quantified (e.g. friendliness score 8/10).
  • Systematically collected — random jottings are not statistics; data must be collected with a plan (Census 2021 used a structured questionnaire).
  • Pre-determined purpose — data collected for a clear goal (e.g. to measure poverty, not just because we are curious).
  • Capable of comparison — statistics allow comparison across time (2021 vs 2011 census) or groups (Bagmati vs Karnali).
  • Affected by multiplicity of causes — prices are affected by supply, demand, money supply, expectations — not one cause alone.
  • Reasonable accuracy — statistics need not be 100% exact; a sample estimate within ±3% is acceptable for policy.

Scope and Importance of Statistics

Statistics is used in almost every field of human activity. In economics, it studies inflation, GDP, balance of payments — Nepal Rastra Bank's Quarterly Economic Bulletin is full of statistics. In planning, NPC uses data on poverty, employment, infrastructure to set targets — e.g. poverty rate 18.7% shapes the Fifteenth Plan target of 11%. In business and management, a tea exporter in Jhapa uses statistics to study demand trends, costs, profits. In state administration, the government uses population, health, education data to allocate budget — Census 2021 said 2.2% of Nepal's population has a disability, so social-security budget rises. In natural sciences, biology uses biostatistics; physics uses error analysis. In social sciences, sociology and psychology use sampling and surveys. In mathematics, statistics is the foundation of probability theory.

Scope of statistics — fields of application with Nepal examples

FieldUse of StatisticsNepal Example
EconomicsInflation, GDP, BOP, employment analysisNRB Economic Bulletin; Economic Survey 2023/24
PlanningTarget-setting, monitoring, evaluationNPC Fifteenth Plan; SDG Status Report
Business & ManagementDemand forecasting, cost-profit analysisTea exporters in Jhapa; NTC market share
State AdministrationBudget allocation, policy designCensus 2021 → federal/provincial budget shares
Natural ScienceBiostatistics, error analysis, experimentsClimatic data of DHM; earthquake intensity
Social ScienceSampling, surveys, attitudinal studiesNLSS, DHS, CBS household surveys
MathematicsProbability, distribution theoryFoundation for statistical inference

Limitations of Statistics

Limitations of statistics and what they mean for students

LimitationExplanationNepal Example
Does not study individualsStatistics studies groups; one person's income is not statisticsA single farmer's income is data point; all farmers' incomes are statistics
Not for qualitative phenomenaHonesty, beauty, intelligence cannot be measured directlyWe can rank "honesty" only by scoring; "Nepali cuisine is tasty" cannot be statistics
Laws not exactStatistical laws are probabilistic, not deterministic like physicsInflation forecast 6% ± 1%, not exactly 6%
Liable to misuseSame data can support opposite conclusions if manipulated"Average income rises" hides that only the rich gained
Only a means, not an endStatistics informs decisions but does not make them; judgement neededPoverty data tells the problem; policy choice is political
Ignores qualitative contextNumbers miss cultural, ethical, historical contextGDP rises but inequality, environment may worsen

Key Statistical Formulas (Mean, Median, Mode)

Mean (arithmetic average) and Median (middle value, grouped data) — Σx = sum of values, n = count, L = lower limit of median class, F = cumulative frequency before median class, f = frequency of median class, h = class width

Mode (most frequent value, grouped data) and Standard Deviation σ (spread of values around mean) — L = lower limit of modal class, f₁ = frequency of modal class, f₀ = previous class frequency, f₂ = next class frequency, h = class width

Cum. Population %Cum. Income %OEqualityLorenzGini gap
Lorenz curve — a graphical statistical tool showing distribution of income (or any variable). The 45° line is perfect equality; the curve below shows inequality. The further the curve bows away from the diagonal, the greater the inequality. Nepal's Gini coefficient (0.30) means moderate inequality.

Beware of Misuse

Statistics can be misused to mislead — the famous saying goes, "There are three kinds of lies: lies, damned lies, and statistics." Examples of misuse: (1) cherry-picking — quoting only the years when GDP grew, hiding recession years; (2) small sample — surveying 10 households in Kathmandu and claiming "all Nepalis support X"; (3) wrong average — using mean income when median is fairer (a few billionaires skew the mean upward); (4) correlation≠causation — saying "ice-cream sales cause drowning" because both rise in summer. Always check: who collected the data, how, why, and what they did not tell you.

Practice Problem

A CBS sample survey of monthly household incomes (in Rs thousand) of 7 households in Kirtipur yielded: 25, 30, 28, 35, 40, 32, 27. Calculate: (a) the arithmetic mean income, (b) the median income, (c) the range, and (d) comment on whether the mean or median better represents the "typical" household.

Practice Problem

Interpret the following statistical statements from the Nepal Economic Survey 2023/24 and explain what each means for a Class 12 student: (i) Nepal's GDP growth in FY 2022/23 was 1.86% (at basic prices), down from 7.6% in 2021/22. (ii) The inflation rate (CPI) averaged 6.83% in 2022/23. (iii) The unemployment rate was 11.4% (NLSS 2017/18), with youth unemployment at 19.3%. (iv) Per-capita GDP rose to USD 1,336 in 2022/23 from USD 1,191 in 2021/22. For each, identify the type of data (cross-section / time-series) and what policy conclusion can be drawn.