Classification, tabulation and frequency distribution

1. Classification

Classification is the process of arranging data into groups or classes according to their common characteristics. It is the first step after collection: it condenses the raw mass, brings out similarities and differences, makes comparison possible and prepares the data for tabulation.

Bases of classification:

• Geographical (spatial): by place — sales by State.
• Chronological (temporal): by time — production by year.
• Qualitative: by attribute — sex, religion, literacy. It may be simple (two classes, e.g. literate and illiterate) or manifold (several attributes at once).
• Quantitative: by a measurable variable — marks, wages, age. This gives a frequency distribution.

2. Frequency distribution: the vocabulary

• Variable: discrete (only whole values, e.g. number of children) or continuous (any value in a range, e.g. height).
• Class limits: the lowest and highest values of a class (in 10–20, the lower limit is 10 and the upper limit 20).
• Class interval (width): upper limit minus lower limit (here 10).
• Mid-point: (lower + upper) ÷ 2 = 15.
• Exclusive method: 0–10, 10–20 … the upper limit is excluded (a value of 10 goes into 10–20). Inclusive method: 0–9, 10–19 … both limits included. Before calculating a median or mode from inclusive classes, convert them to exclusive by subtracting 0.5 from each lower limit and adding 0.5 to each upper limit (9.5–19.5 …).
• Open-end classes: “below 10” or “60 and above”.
• Cumulative frequency: running total, “less than” or “more than”.

3. Problem: building a frequency distribution (January 2025)

Prepare a frequency distribution for the following 40 observations with a class interval of 10: 16, 12, 30, 29, 22, 35, 39, 40, 42, 40, 50, 30, 18, 12, 5, 15, 3, 4, 9, 45, 9, 0, 5, 6, 8, 15, 25, 22, 3, 4, 8, 12, 5, 9, 3, 4, 30, 32, 29, 1.

Smallest value 0, largest 50, so exclusive classes 0–10 to 50–60 cover the range. Go through the figures in order and put a tally mark against the class for each one (a value of 10, 20, 30… goes into the class that begins with it).

Check: the frequencies add up to 40, the number of observations. In the exam, show a tally column (groups of four strokes crossed by a fifth) instead of listing the values; examiners give a mark for it.

4. Tabulation

Tabulation is the systematic arrangement of classified data in rows and columns. It simplifies data, saves space, makes comparison easy, shows the totals, and is the basis for analysis and diagrams.

Parts of a good table (the January 2026 and June 2025 short note):

1. Table number for reference.
2. Title: short and complete — what, where, when (“Students of X College by faculty and gender, 2009 and 2010”).
3. Head note: below the title, the unit of measurement (“in Rs. lakh”).
4. Captions: column headings.
5. Stubs: row headings.
6. Body: the figures.
7. Footnote: explanations or exceptions.
8. Source note: where secondary data came from.

Rules: keep it simple, arrange items logically (alphabetical, chronological or by size), show totals, avoid abbreviations and ditto marks, and rule off columns clearly. Types: simple (one characteristic), two-way, three-way and manifold (several characteristics); general-purpose (reference) and special-purpose (summary) tables.

5. Problem: the blank table (January 2026, January 2025)

Prepare a blank table to show the distribution of students of a college according to (i) faculty: Arts, Commerce and Science; (ii) gender: male and female; (iii) year: 2009 and 2010.

Table 1: Students of ____ College by faculty, gender and year, 2009 and 2010 (number of students)

Source: college records. The same pattern answers the 100-mark January 2026 variant (population of a town by sex, religion — Hindu, Muslim, Christian — and years 2018 and 2019): put religion in the stub, years as the main captions and male, female, total under each year, adding an “Others” row if you wish and a grand total row.

How this is examined

The blank table appeared in January 2026, January 2025 and the 100-mark January 2026 paper; “Write a short note on the components of a good table” in January 2026 and “Write a short note on tabulation” in June 2025. The frequency-distribution problem (with histogram) was the ten-mark Unit I question in January 2025. Count your tallies twice; the total must equal the number of observations.