Once data have been collected, they are usually in the form of raw, unorganised numbers called raw data. A raw mass of figures is difficult to read, compare or interpret. The next step in a statistical study is therefore to organise the data - to classify and arrange them in a systematic way so that their essential features become clear. This process of organisation converts raw data into a frequency distribution, which is the basis for all further statistical analysis.
Organisation of data involves three related operations: editing, classification and tabulation. Editing removes errors and inconsistencies in the raw data. Classification groups the data into classes according to their common characteristics. Tabulation presents the classified data in the form of statistical tables with rows and columns. Together these operations make the data concise, comparable and ready for analysis.
This chapter deals with the meaning and types of classification, the variable and its types, the construction of a frequency distribution - including continuous frequency distributions, class limits, class intervals, class size and mid-values - and the ways of preparing discrete and continuous series from raw data.
2. Meaning and Objectives of Organisation of Data
Organisation of data is the process of arranging raw data in a systematic order to make them understandable and usable. Raw data are the data in their original, unprocessed form as collected from the field. For example, the daily collection of a milk dairy may be: 2, 3, 2, 4, 5, 2, 3, 4, 5, 2 ... In this form the figures convey very little.
The objectives of organising data are:
To reduce the size and complexity of the data.
To convert the data into a form that is easy to read, understand and remember.
To make the data comparable.
To reveal the patterns and trends hidden in the data.
To prepare the data for further statistical treatment such as the computation of averages, dispersion and correlation.
The two main steps of organisation are classification and tabulation. Classification is the grouping of data into classes or categories on the basis of common characteristics; tabulation is the presentation of this classified data in a table.
3. Types of Classification
Classification may be of the following types, depending on the basis adopted:
Chronological or temporal classification: Data are classified according to time, e.g. production of wheat from 2015 to 2025. This is also called time series classification.
Geographical or spatial classification: Data are classified according to place or location, e.g. state-wise production of rice.
Qualitative classification: Data are classified according to attributes or qualities that cannot be measured numerically, e.g. literacy, sex, occupation, religion. These categories are called attributes.
Quantitative classification: Data are classified according to numerical values of a characteristic, e.g. marks, income, age, height. This gives rise to a frequency distribution.
4. Variables and their Types
A characteristic that takes different values in different individuals or units is called a variable. The value of the variable changes from unit to unit; for example, marks scored by students in a class, height of plants, or income of families.
Variables are of two types:
Discrete variable: A variable that can take only certain specific values, generally whole numbers, with no possible values between them, is called a discrete variable. Examples are the number of students in a class, the number of members in a family, and the number of cars in a household. Discrete variables usually arise from counting.
Continuous variable: A variable that can take any value between any two given values is called a continuous variable. It can assume an infinite number of values within a range. Examples are height, weight, temperature, time and distance. Continuous variables arise from measurement.
Because a continuous variable can take any value, its data are grouped into class intervals. For example, heights are expressed in ranges such as 150-155 cm, 155-160 cm, etc.
5. Frequency and Frequency Distribution
The frequency of a particular value of a variable is the number of times that value occurs in the data. If the value 3 occurs 5 times in a set of observations, its frequency is 5. The total of all frequencies is equal to the total number of observations.
A frequency distribution is a table that presents the values of a variable (or class intervals) along with their corresponding frequencies. Frequency distributions may be of two types:
Discrete (ungrouped) frequency distribution: In this distribution the individual values of a discrete variable are listed with their frequencies. For example, the number of members in 20 families may be presented as: 1, 2, 3, 4, 5 with frequencies 2, 5, 8, 3, 2.
Continuous (grouped) frequency distribution: In this distribution the range of a continuous variable is divided into class intervals, and the number of observations falling in each class is counted. For example, marks of students may be grouped as 0-10, 10-20, 20-30, and so on, with their frequencies.
6. Construction of a Continuous Frequency Distribution
A continuous frequency distribution is constructed through the following steps:
Find the range of the data: Range = Maximum value - Minimum value.
Decide the number of classes. A convenient number is usually between 5 and 15; Sturges' rule suggests that the number of classes = 1 + 3.322 log N, where N is the number of observations.
Decide the size (width) of each class interval: Class size = Range / Number of classes.
Decide the class limits - the lower and upper boundaries of each class. Class limits should be chosen so that every observation falls in exactly one class.
Prepare the tally marks and count the frequency of each class.
The important terms used in a continuous frequency distribution are:
Class limits: The lowest and highest values that can be included in a class are called the lower limit and upper limit of that class.
Class interval: The span or width of a class, i.e. the difference between the upper and lower limits of the class, is the class interval.
Mid-value or class mark: The midpoint of a class is called its mid-value. It is given by: Mid-value = (Lower limit + Upper limit) / 2.
Frequency: The number of observations falling in a class is its frequency.
7. Continuous and Discrete Series with Exclusive and Inclusive Classes
A discrete series shows the individual values of a variable with their frequencies. A continuous series shows class intervals with their frequencies.
Class intervals may be of two types:
Exclusive classes: In exclusive classes, the upper limit of one class is the lower limit of the next class, and the upper limit of each class is excluded from that class but included in the next class. For example, in classes 0-10, 10-20, 20-30, the value 10 belongs to the class 10-20, not to 0-10. This type removes ambiguity about where a value belongs, and the class interval equals the difference between successive lower limits. The mid-value is correctly given by (lower + upper)/2.
Inclusive classes: In inclusive classes, both the lower and upper limits are included in the class, e.g. classes 0-9, 10-19, 20-29. Here there are no gaps between classes. When converting inclusive classes to exclusive classes for computation of mid-values, 0.5 is subtracted from the lower limits and 0.5 added to the upper limits.
8. Presentation of Data in Series
The following series are commonly used:
Individual series: The data are presented as individual observations, e.g. marks of 10 students: 45, 50, 62, ... This is suitable for small sets of data.
Discrete series: Values of a discrete variable are presented with their frequencies, e.g. number of children per family and the number of families having each value.
Continuous series: Class intervals with frequencies are presented, e.g. income classes and the number of households in each class.
Cumulative frequency series: The frequencies are cumulated either from below (less than series) or from above (more than series). The cumulative frequency of a class is the sum of the frequencies of that class and all preceding classes. Cumulative frequencies are useful for computing medians, quartiles and drawing ogives.
Quick Revision Tables
Type of Classification
Basis
Example
Chronological
Time
Production of wheat 2015-2025
Geographical
Place
State-wise production of rice
Qualitative
Attributes
Sex, literacy, occupation
Quantitative
Numerical values
Marks, income, age
Term
Definition
Formula
Frequency
Number of times a value occurs
f
Range
Difference of max and min
Range = Max - Min
Class interval
Width of a class
Upper limit - Lower limit
Mid-value
Midpoint of a class
(L + U) / 2
Number of classes
Sturges' rule
1 + 3.322 log N
Mind Map
graph TD
A["ORGANISATION OF DATA"] --> B["Classification"]
A --> C["Tabulation"]
A --> D["Variables"]
A --> E["Frequency distribution"]
B --> B1["Chronological - time"]
B --> B2["Geographical - place"]
B --> B3["Qualitative - attributes"]
B --> B4["Quantitative - numerical"]
D --> D1["Discrete - counting, whole numbers"]
D --> D2["Continuous - measurement, any value"]
E --> E1["Discrete frequency distribution"]
E --> E2["Continuous frequency distribution"]
E2 --> F["Class limits, interval, mid-value, frequency"]
E2 --> G["Exclusive vs inclusive classes"]
E --> H["Cumulative frequency - less than / more than"]
Important Diagrams (SVG)
Diagram 1: Types of Variables and Classification of Data
Diagram 2: Continuous Frequency Distribution - Class Terms
Common Mistakes
Confusing discrete and continuous variables; discrete variables take only specific whole values (from counting), while continuous variables take any value (from measurement).
Forgetting that the mid-value is (Lower + Upper) / 2, not the difference between limits.
Using inclusive classes without converting them to exclusive classes when computing mid-values and continuous statistical measures.
Believing that the upper limit is included in an exclusive class; in exclusive classes the upper limit belongs to the next class.
Computing the range incorrectly; Range = Maximum value - Minimum value of the entire data.
Choosing too many or too few classes; a convenient number is usually 5 to 15, following Sturges' rule when needed.
Confusing cumulative frequency with simple frequency; cumulative frequency is the running total of frequencies up to a class.
Exam Tips
Define raw data and state the objectives of organising data.
Distinguish among chronological, geographical, qualitative and quantitative classification with examples.
Explain discrete and continuous variables with suitable examples and state which are grouped into class intervals.
Define frequency and construct a discrete and a continuous frequency distribution from given raw data.
State the formulas: Range = Max - Min; Mid-value = (L + U) / 2; Number of classes = 1 + 3.322 log N.
Differentiate between exclusive and inclusive classes and explain how to convert one into the other.
Define cumulative frequency and explain 'less than' and 'more than' series.
Conclusion
In this chapter we learned how to organise raw data so that it becomes meaningful. We studied the objectives of organisation, the four types of classification - chronological, geographical, qualitative and quantitative - and the concept of the variable with its two forms, discrete and continuous. We defined frequency and constructed discrete and continuous frequency distributions, learning the important terms of class limits, class interval, mid-value and cumulative frequency. We also understood the difference between exclusive and inclusive classes and how to convert inclusive classes into exclusive ones. This organised data, in the form of frequency distributions, is the raw material for the next stage of statistical analysis - the presentation of data through tables and diagrams - and for the computation of the statistical measures studied in the later chapters.