COLOUR THEME
Objectives and types of classification, frequency distribution terms, the four scales of measurement (NOIR) and parts of a table.
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Classification is the process of arranging data into groups or classes according to common characteristics. Raw data are a heap of numbers; classified data are concise, comparable and ready for tabulation and graphing. Classification is the first step after collection and editing, and the step before tabulation.
In brief
Condense large data into a small, understandable form. Bring out similarities and differences between groups. Make comparison possible. Prepare data for tabulation, graphs…
Condense large data into a small, understandable form.
Bring out similarities and differences between groups.
Make comparison possible.
Prepare data for tabulation, graphs and statistical analysis.
In brief
Type Basis Example Geographical (spatial) Place State-wise population, district-wise rainfall Chronological (temporal) Time Year-wise student enrolment Qualitative Attribute…
| Type | Basis | Example |
|---|---|---|
| Geographical (spatial) | Place | State-wise population, district-wise rainfall |
| Chronological (temporal) | Time | Year-wise student enrolment |
| Qualitative | Attribute (cannot be measured numerically) | Gender, religion, marital status, literacy |
| Quantitative | Measurable variable | Age groups, income groups, marks ranges |
Quantitative classification gives a frequency distribution. Qualitative classification gives groups by attribute and can be simple (two classes such as male and female, called dichotomous) or manifold (many classes).
In brief
A variable is a characteristic that can take different numerical values.
A variable is a characteristic that can take different numerical values. A discrete variable takes only whole or separate values (number of students, number of cars). A continuous variable can take any value in a range (height, weight, time, temperature). An attribute is a qualitative characteristic that is described, not measured (honesty, colour, religion).
In brief
Covers Class interval, Class limits, Class width (size), Class mark (midpoint), Frequency and more.
Class interval: the range of one group, for example 10 to 20.
Class limits: the lower limit and upper limit of a class.
Class width (size): upper limit minus lower limit.
Class mark (midpoint): the average of the two limits.
Frequency: the number of observations in a class.
Cumulative frequency: the running total of frequencies. "Less than" cumulative adds from the top class downward, and "more than" cumulative adds from the bottom.
Relative frequency: class frequency divided by the total frequency, often shown as a percentage.
Frequency density: frequency divided by class width. It is plotted when class widths are unequal.
\text{Class width} = \text{Upper limit} - \text{Lower limit}
\text{Class mark} = \frac{\text{Lower limit} + \text{Upper limit}}{2}
Exclusive method: the upper limit of a class is not included in that class (10 to 20, 20 to 30; a value of 20 goes into the second class). Inclusive method: both limits are included (10 to 19, 20 to 29). For inclusive classes, adjust to true class boundaries by subtracting 0.5 from the lower limit and adding 0.5 to the upper limit before drawing a histogram.
In brief
Scale Property Operations allowed Example N ominal Names or categories only Counting, mode Gender, blood group, religion O rdinal Order, but unequal gaps Ranking, median…
| Scale | Property | Operations allowed | Example |
|---|---|---|---|
| Nominal | Names or categories only | Counting, mode | Gender, blood group, religion |
| Ordinal | Order, but unequal gaps | Ranking, median | Class rank, grades, Likert scale |
| Interval | Equal gaps, no true zero | Addition, subtraction, mean | Temperature in Celsius, calendar year |
| Ratio | Equal gaps and a true zero | All operations, ratios | Height, weight, income, age |
A fast test: if "twice as much" makes sense, it is a ratio scale (40 kg is twice 20 kg). It does not make sense for Celsius (40°C is not twice as hot as 20°C), so that is an interval scale.
In brief
Tabulation is the systematic arrangement of classified data in rows and columns.
Tabulation is the systematic arrangement of classified data in rows and columns. The parts are: table number, title, caption (column headings), stub (row headings), body (the figures), headnote (units or notes below the title), footnote (explanations at the bottom), and source note. Tables can be simple (one characteristic), double or two-way (two characteristics), and complex or multi-way (more than two).
In brief
Example 1.
Example 1. A class interval is 30 to 40. Find its class width and class mark. Answer: width = 40 − 30 = 10; class mark = (30 + 40) / 2 = 35.
Example 2. Frequencies of five classes are 4, 7, 12, 9, 3. Find the cumulative frequencies. Answer: 4, 11, 23, 32, 35.
Example 3. Classify these as discrete or continuous: number of books in a library, weight of a bag, number of accidents, distance travelled. Answer: discrete are books and accidents; continuous are weight and distance.
Example 4. "Marital status of a population" is which type of classification? Answer: qualitative, and manifold if more than two categories are used.
Example 5. Student rank in a class is measured on which scale? Answer: ordinal.
Practise with free MCQs and answer keys, then return here to fix what you got wrong.
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