Unit 2: Classification and presentation of data
Fundamental of Statistics notes · PTU syllabus (UGCC2504)
On this page
Unit summary
Raw data is a jumble of numbers. Before it can be analysed it must be arranged in a meaningful way. This unit covers classification (grouping data), tabulation (arranging it in tables) and presentation through diagrams and graphs.
After this unit you can
- State the objectives of classification and classify data by different bases
- Construct a frequency distribution and a statistical table with all its parts
- Choose and draw suitable diagrams for given data
- Draw a histogram, frequency polygon and ogive
PTU syllabus topics
- Classification objectives and methods
- tabular presentation (components of a statistical table, construction rules, types of tables)
- diagrammatic and graphic presentation — types of diagrams and graphs
Tables
Title, stub, caption, body, footnote
Bar diagrams
Simple, multiple and component bars
Pie chart
Parts of a whole as sectors
Histogram
Frequency of continuous classes
Frequency polygon and ogive
Line graphs of frequencies and cumulative frequencies
Topic 1
Classification of data
Classification is the process of arranging data into groups or classes according to their common characteristics. Objectives: to simplify data, bring out similarities, allow comparison and prepare data for tabulation and analysis.
Geographical
By place: state-wise sales
Chronological
By time: year-wise production
Qualitative
By attribute: gender, literacy
Quantitative
By measurable size: marks, income
A frequency distribution shows how many times each value or class occurs. In exclusive classes (0–10, 10–20) the upper limit is excluded; in inclusive classes (0–9, 10–19) both limits are included.
- Class interval = upper limit − lower limit; mid-value = (lower + upper) / 2.
Topic 2
Tabulation: parts of a statistical table
Tabulation is the orderly arrangement of data in rows and columns.
| Part | What it contains |
|---|---|
| Table number | For reference |
| Title | What, where and when the data relates to |
| Head note | Units of measurement |
| Captions | Column headings |
| Stubs | Row headings |
| Body | The actual figures |
| Footnote | Clarifications |
| Source note | Where the data came from |
Rules: the title should be short and clear, units must be stated, totals should be given, and the table should not be overcrowded. Types of tables: simple (one-way) — one characteristic; double (two-way) — two characteristics; complex (manifold) — three or more.
Topic 3
Diagrammatic presentation
Diagrams make data attractive and easy to compare at a glance.
Simple bar
One series of values
Sales in five years
Multiple bar
Comparing two or more series side by side
Sales of two products by year
Sub-divided bar
Parts making up a total
Expenditure split by head
Percentage bar
Shares in percent
Budget share by item
Pie chart
Parts of a whole as angles
Market share
Example
For a pie chart, angle of a component = (component value / total) × 360°. If rent is ₹3,000 of ₹12,000, its angle is 90°.
Topic 4
Graphic presentation
Graphs are used for frequency distributions and time series.
- Histogram: adjacent rectangles for a continuous frequency distribution; height shows frequency.
- Frequency polygon: joins the mid-points of the tops of the histogram bars.
- Frequency curve: a smoothed frequency polygon.
- Ogive (cumulative frequency curve): "less than" ogive uses upper limits and cumulative frequencies; "more than" ogive uses lower limits. The two ogives cross at the median.
Exam tip
The intersection of the two ogives gives the median — a favourite graphical question.
Key terms
- Classification
- Grouping data by common characteristics
- Frequency distribution
- A table showing how often each value or class occurs
- Tabulation
- Arranging data in rows and columns
- Histogram
- Bar graph of a continuous frequency distribution
- Ogive
- A cumulative frequency curve
Quick revision
- Bases: geographical, chronological, qualitative, quantitative.
- Table parts: number, title, head note, captions, stubs, body, footnote, source.
- Pie angle = value / total × 360°.
- Ogives meet at the median.
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 classification and state its objectives.
- Q2.Differentiate between exclusive and inclusive class intervals.
- Q3.What is a stub and a caption?
- Q4.What is an ogive?
- Q5.How is the angle of a pie chart component calculated?
Long-answer questions
- Q1.Explain the parts of a statistical table and the rules for constructing it.
- Q2.Explain the different types of diagrams with suitable examples.
- Q3.Draw a histogram and frequency polygon for a frequency distribution of your choice and explain each.
- Q4.Explain "less than" and "more than" ogives and how the median is located from them.
Stuck on this unit?
Message SBS on WhatsApp for help with Fundamental of Statistics, or to ask about studying BCA at Synetic.