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Meaning, Characteristics and Scope of Statistics, ISC 11

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EconomicsISC Class 11 · Introduction to Statistics

Meaning, Characteristics and Scope of Statistics (ISC Class 11 Economics)

Updated 17 October 2026 · Fact-checked

In the plural sense, statistics means numerical data (facts expressed in numbers); in the singular sense, it is the science of collecting, organising, presenting, analysing and interpreting numerical data. Statistical data are aggregates of facts, affected by many causes, numerically expressed, reasonably accurate, collected systematically for a purpose and comparable. Its scope covers descriptive and inferential methods.

Statistics as a science moves through five stages; the first three describe the data, the last two draw conclusions from it.

Illustration drawn for QuestionBuddy.

Understand Statistics: Meaning, Characteristics and Scope

Statistics in the plural sense. Numerical facts collected about some subject: sales figures, population, prices. A single figure is not statistics; a set of related figures is.

Statistics in the singular sense. A science (method) that deals with collection, organisation, presentation, analysis and interpretation of data. Stages: *collection, organisation, presentation, analysis, interpretation.*

Characteristics of statistics as numerical data.
1. *Aggregate of facts:* a single figure (one student's marks) is not statistics.
2. *Affected by multiple causes:* sales are affected by price, income, season, taste.
3. *Numerically expressed:* qualitative facts (honesty) must be converted to numbers (ranks, scores).
4. *Reasonably accurate:* an acceptable degree of accuracy for the purpose.
5. *Collected systematically for a pre-determined purpose.*
6. *Comparable:* data must be of the same kind, in the same units, to compare.
7. *Placed in relation to each other:* related to the same subject.

Functions and scope.

  • *Descriptive statistics:* collect, organise and summarise (tables, diagrams, averages).
  • *Inferential statistics:* draw conclusions about a population from a sample, forecast and test relations.
  • Simplifies complex data; helps comparison; shows relationships; supports policy and forecasting.
  • Applies in economics, business, government, science and daily life.

Statistics and economics. Economics uses data on income, prices, output; statistics provides the methods to test economic theories and plan policy.

Types of data (preview). Primary and secondary; discrete and continuous.

Statistics: Meaning, Characteristics and Scope: key facts

Stages
  • Collection
  • Organisation
  • Presentation
  • Analysis
  • Interpretation
Singular sense.
Two senses
Plural: numerical data | Singular: science of method
Meaning.
Branches
Descriptive: summarise | Inferential: conclude from sample
Scope.

How to answer Statistics: Meaning, Characteristics and Scope questions

Decide the sense in which the word is used and test the data against the characteristics.

  1. 1Plural sense: are there aggregates of numerical facts?
  2. 2Singular sense: is it a method or study?
  3. 3Test data for each characteristic (aggregate, numerical, comparable).
  4. 4State the branch: descriptive or inferential.

Statistics: Meaning, Characteristics and Scope in real life

The idea, met in an everyday situation. Answer the question in your own words, then compare with the model answer. The one-line hook is what to remember.

Is it statistics?

Suppose a headline says "A student scored 85 in mathematics", while another gives the marks of all 40 students in the class.

Which is statistics and why?

Try it first, then show the solutionSolution
  1. A single figure is not an aggregate.
  2. Marks of all 40 students form an aggregate of related facts that can be compared and averaged.

Answer: The 40 marks are statistics; the single figure is not.

Memory hook: Statistics needs many facts.

Tricks to remember Statistics: Meaning, Characteristics and Scope

Short memory aids. Say each one aloud once, then use it on a question the same day.

  • Two senses

    Plural = numbers; singular = science.

    Use it when: Meaning.

  • C-O-P-A-I

    Collect, Organise, Present, Analyse, Interpret.

    Use it when: Stages.

  • Aggregate, many causes, numbers

    Key characteristics.

    Use it when: Features.

Statistics: Meaning, Characteristics and Scope: solved examples

Ordered from board level to HOTS. Try each one before you open the solution.

Example 1: Sense of statistics · 1 mark · MCQBoard level

"Statistics are collected for the purpose of planning." Here the word statistics is used in the:
(a) singular sense (b) plural sense (c) both (d) neither

Try it first, then show the solutionSolution
  1. The sentence refers to numerical data: plural sense.

Answer: (b) plural sense

Example 2: Characteristics · 4 marks · Short answerBoard level

State any four characteristics of statistics as numerical data. (4 marks)

Try it first, then show the solutionSolution
  1. Aggregate of facts.
  2. Affected by multiple causes.
  3. Numerically expressed.
  4. Collected systematically for a purpose.

Answer: Statistics are aggregates of facts, affected by several causes, expressed numerically and collected systematically for a purpose.

Example 3: Test the data · 6 marks · Long answerHarder board level

State, with a reason, which of these is statistics in the plural sense: (i) a firm's sales in each of the last 5 years: Rs 12, 14, 15, 18, 20 lakh; (ii) one student's height of 160 cm; (iii) "The weather is hot"; (iv) the prices of 10 commodities in 2020 and 2024. Find the percentage growth of the firm's sales between the first and last year and the average annual increase. (6 marks)

Try it first, then show the solutionSolution
  1. (i) Yes: related aggregate in numbers; (ii) No: single fact; (iii) No: qualitative; (iv) Yes: related, comparable aggregates.
  2. Growth in sales = (20 - 12) / 12 x 100 = 66.67%.
  3. Average annual increase = (20 - 12) / 4 = Rs 2 lakh.

Answer: (i) and (iv) are statistics; (ii) and (iii) are not. Sales grew 66.67% in 4 years, an average increase of Rs 2 lakh a year.

Example 4: Descriptive and inferential · 5 marks · Long answerHarder board level

A researcher records the marks of 200 students, then computes the average (62) and the highest (96); then she uses a sample of 40 to estimate the average of all 2,000 students in the district. Classify each activity, and find the number of students whose marks are summarised, and the sampling fraction. (5 marks)

Try it first, then show the solutionSolution
  1. Recording marks and computing the average and highest: descriptive statistics.
  2. Estimating the district average from a sample: inferential statistics.
  3. Number summarised in the first activity = 200.
  4. Sampling fraction = 40 / 2,000 = 2%.

Answer: Descriptive for the 200 students; inferential for the sample of 40; sampling fraction 2%.

Example 5: Misuse · 4 marks · Short answerHOTS / competency

A shop advertises "Our average customer saves Rs 500", but 3 customers saved Rs 5,000 each and 97 saved nothing. Find the true average saving and the percentage who saved anything; explain which characteristic of statistics (accuracy, comparability) the advertisement ignores. (4 marks)

Try it first, then show the solutionSolution
  1. Total saving = 3 x 5,000 = Rs 15,000; average over 100 customers = Rs 150.
  2. Only 3% of customers saved anything.
  3. The claim of Rs 500 is not reasonably accurate or representative; the average hides the pattern.
  4. Statistics need a clear base and an honest description of the distribution.

Answer: The true average is Rs 150, and only 3% saved; the claim is inaccurate and misleading.

Where students lose marks in Statistics: Meaning, Characteristics and Scope

The slips examiners see most often, and what to write instead.

  • Mistake: Treating a single fact as statistics

    Using the plural word loosely.

    Wrong working

    One student's marks is statistics

    Right working

    An aggregate is needed

    Do this: Look for related facts.

    Usually costs: 1 mark.

  • Mistake: Confusing the two senses

    Same word.

    Wrong working

    Singular sense means data

    Right working

    Singular means the science of method

    Do this: Plural = data; singular = science.

    Usually costs: 1-2 marks.

  • Mistake: Listing only collection and presentation as stages

    Incomplete.

    Wrong working

    Collection, presentation

    Right working

    Five stages

    Do this: List all five.

    Usually costs: 1 mark.

Exam tips

  • Give one numerical example for the plural sense.
  • Name the five stages in order.
  • Mention both descriptive and inferential branches.

Practice questions on Statistics: Meaning, Characteristics and Scope

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

  1. Q1 · 1 mark · MCQBoard level

    Which of the following is NOT a characteristic of statistics as data?
    (a) aggregate of facts (b) qualitative description only (c) numerically expressed (d) collected for a purpose

    Hint

    Statistics are numerical.

    Answer

    (b) qualitative description only

  2. Q2 · 3 marks · Short answerBoard level

    Distinguish between descriptive and inferential statistics with an example of each. (3 marks)

    Hint

    Summarise versus conclude.

    Answer

    Descriptive statistics summarises data (the average income of 100 families); inferential statistics draws conclusions about a population from a sample (estimating the average income of a city from a sample).

  3. Q3 · 4 marks · Short answerHarder board level

    Marks of 8 students: 56, 64, 70, 48, 90, 62, 75, 55. Treat them as statistics, find the range, the mean and the percentage of students scoring above the mean. (4 marks)

    Hint

    Sum = 520.

    Answer

    Range = 90 - 48 = 42; mean = 520 / 8 = 65; students above 65: 70, 90, 75 = 3 out of 8 = 37.5%.

  4. Q4 · 4 marks · Short answerHarder board level

    The sales of a firm over four years (Rs lakh): 40, 46, 55, 66. Find the yearly growth rates (to one decimal) and the average of the growth rates, and say whether the series is rising at an increasing rate. (4 marks)

    Hint

    6/40, 9/46, 11/55.

    Answer

    Growth: 6 / 40 = 15.0%; 9 / 46 = 19.6%; 11 / 55 = 20.0%. Average = 18.2%. The growth rate is rising, so sales rise at an increasing rate.

  5. Q5 · 3 marks · Short answerHOTS / competency

    A politician says, "Statistics can prove anything." Evaluate in three points, using the characteristics of statistics. (3 marks)

    Hint

    Misuse versus method.

    Answer

    Statistics can be misused by choosing a biased sample or an unsuitable average; but honest statistics, collected systematically and compared on the same basis, are reliable. The fault lies in the user, not the method.

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

  1. 1.Plural sense means?Show answer

    Numerical data.

  2. 2.Singular sense means?Show answer

    The science of method.

  3. 3.Stages?Show answer

    Collection, organisation, presentation, analysis, interpretation.

  4. 4.A single figure is?Show answer

    Not statistics.

  5. 5.Inferential statistics uses?Show answer

    Samples to draw conclusions.

Statistics: Meaning, Characteristics and Scope: frequently asked questions

Is statistics a science or art?

Both.

Do statistics need numbers?

Yes, numerically expressed.

Is probability part of it?

Used in inference.

Who uses statistics?

Governments, firms and researchers.