Given facts and figures is known as data.


    There are two uses of the word statistics
  1. In plural sense, statistics means data.
  2. In singular sense, statistics is the science which deals with the collection, presentation, analysis and interpretation of the data.

Raw data

Data obtained in original form is called raw data.


Arranging the numerical facts and figures in the ascending or descending order is called an array.

Tabulation or presentation of data

Arranging the data in tabular form is called tabulation or presentation of data.


Each numerical figure in a data is called an observation.


The number of times a particular observation occurs is called it frequency.

Grouped frequency distribution

When the data contains a large number of observations, we put them in different groups called class intervals.
    They take two forms.
  1. Inclusive form is written such as 0-10, 11-20, 21-30 etc. means 0 to 10, 11 to 20, 21 to 30 etc. Here 0-10 means between 0 and 10 including both 0 and 10. 0 is called the lower limit and 10 is called the upper limit of the class 0-10.
  2. Exclusive form is written such as 0-10, 10-20, 20-30 etc. Here lower limit is included and the upper limit is excluded. Thus 0 - 10 would mean 0 and more but less than 10. 10-20 would mean 10 or more but less than 20.

Class Interval and class boundaries

Each group into which the raw data is condensed is called a class interval. In exclusive form the lower and the upper limits are called the class boundaries or True lower limit and True upper Limit of the class respectively. In inclusive form the boundaries are obtained by subtracting 0.5 from the lower limit and adding 0.5 to upper limit.

Class Size

Difference between true upper limit and true lower limit is called the class size.

Class Mark or Mid-value

The average of the upper limit and lower limit is called the class mark.
Class Mark = (1/2)(upper limit + lower limit)


The difference between the maximum value and the minimum value of the observations is called its range.