Unit 1: Introduction to statistics & sampling
Business Statistics notes · PTU syllabus (BCOMGE 201-18)
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Unit summary
Business decisions rely on numbers — sales trends, customer surveys, quality checks. Statistics provides the tools to collect, organise and interpret such data. This unit covers the meaning, features, importance, functions, scope and limitations of statistics, sources and presentation of data, frequency distributions, populations and samples, descriptive and inferential statistics, and sampling methods.
After this unit you can
- Define statistics and explain its features, importance and scope in business
- Distinguish primary and secondary data and build frequency distributions
- Distinguish population and sample and descriptive and inferential statistics
- Explain probability and non-probability sampling methods
PTU syllabus topics
- Meaning
- features
- importance
- functions
- scope and limitations of statistics
- sources of primary and secondary data
- presentation of data
- frequency distribution
- population and sample
- descriptive and inferential statistics
- probability and non-probability sampling methods
Simple random
Every member has an equal chance
Stratified
Random samples from each subgroup
Systematic
Every kth member
Cluster
Randomly chosen groups
Non-probability
Convenience, judgement, quota
Topic 1
Meaning, features, importance, functions and scope
Statistics (singular) is the science of collecting, classifying, presenting, analysing and interpreting numerical data. Statistics (plural) are numerical facts collected for a purpose. Features (Secrist): aggregates of facts, numerically expressed, affected by multiple causes, collected systematically for a purpose, reasonably accurate and comparable. Importance in business: market research, demand forecasting, quality control, financial analysis, HR analytics (attrition, performance) and decision-making under uncertainty. Limitations: studies only quantitative data and groups (not individuals), results are true on average, and data can be misused.
- 1
Presents facts in definite form
- 2
Simplifies mass data
- 3
Facilitates comparison
- 4
Helps in formulating and testing hypotheses
- 5
Helps in prediction and forecasting
- 6
Helps in policy formulation
Topic 2
Sources of data
Meaning
Collected first-hand for the purpose
Already collected by others
Methods/sources
Surveys, interviews, observation, experiments
Government reports, RBI bulletins, company reports, websites
Cost and time
High
Low
Reliability for the purpose
High
Must be checked
Topic 3
Presentation of data
Collected data is presented so that it can be understood at a glance.
- Textual presentation: data described in paragraphs — suitable only for small data.
- Tabular presentation: data in rows and columns. Parts of a table: table number, title, caption (column headings), stub (row headings), body, head note and footnote/source.
- Diagrammatic presentation: simple, multiple, sub-divided and percentage bar diagrams; pie charts; pictograms.
- Graphic presentation: histogram, frequency polygon, frequency curve and ogive (cumulative frequency curve — used to locate the median graphically).
Used for
Comparisons between categories
Frequency distributions and time series
Drawn on
Plain paper
Graph paper
Examples
Bar diagram, pie chart
Histogram, ogive, line graph
Exam tip
A table should be self-explanatory; always write the title, units and source — examiners deduct marks for missing them.
Topic 4
Frequency distribution
A frequency distribution groups data into classes and shows how many observations fall into each.
| Marks | Number of students |
|---|---|
| 0–20 | 4 |
| 20–40 | 10 |
| 40–60 | 18 |
| 60–80 | 12 |
| 80–100 | 6 |
Key terms: class limits, class interval (width), mid-value, frequency and cumulative frequency. A good distribution has 5–15 classes of equal width.
Topic 5
Population, sample, descriptive and inferential statistics
- Population (universe): the whole group under study (all customers of a bank).
- Sample: a part of the population selected for study. A parameter describes a population; a statistic describes a sample.
- Descriptive statistics summarise data (averages, charts). Inferential statistics draw conclusions about a population from a sample (estimation, hypothesis testing).
Topic 6
Sampling methods
Probability: simple random
Every unit has an equal chance (lottery, random numbers)
Probability: stratified
Divide into strata, sample each
Probability: systematic
Every kth unit
Probability: cluster
Randomly choose whole groups
Non-probability: convenience, judgement, quota, snowball
Chosen by ease or judgement
Exam tip
Probability sampling allows results to be generalised to the population; non-probability sampling is quicker and cheaper but may be biased.
Key terms
- Statistics
- The science of collecting and analysing numerical data
- Population
- The entire group under study
- Sample
- A subset of the population
- Parameter
- A measure describing a population
- Stratified sampling
- Sampling separately from each subgroup
Quick revision
- Primary = first-hand; secondary = already published.
- Parameter (population) vs statistic (sample).
- Descriptive summarises; inferential generalises.
- Probability: random, stratified, systematic, cluster.
Important exam questions
Practice questions written to the PTU exam pattern for this unit's syllabus: short answers (Section A style) and long answers (Sections B and C style).
Short-answer questions
- Q1.Define statistics and list two limitations.
- Q2.Differentiate between primary and secondary data.
- Q3.Differentiate between population and sample.
- Q4.What is inferential statistics?
- Q5.What is systematic sampling?
Long-answer questions
- Q1.Explain the importance and scope of statistics in business.
- Q2.Explain the construction of a frequency distribution with an example.
- Q3.Explain probability and non-probability sampling methods.
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