Data Handling - Organising and Grouping Data (Frequency Distribution)

Raw Data and Array: Data collected in its original form is called raw data. When this data is arranged in ascending or descending order of magnitude, it is called an 'Arrayed Data' or an 'Array'. This helps in identifying the minimum and maximum values quickly.

Frequency and Tally Marks: The number of times a particular observation occurs in a data set is called its frequency. To record frequencies, we use tally marks where each occurrence is marked by a vertical bar $|$. To represent 5, four vertical bars are drawn and a fifth diagonal line crosses through them, visually forming a 'bundle' of five for easy counting.

Frequency Distribution Table: This is a tabular arrangement that shows the frequency of each observation or class interval. A standard table consists of three columns: the variable (or class), the tally marks, and the frequency ($f$). The sum of all frequencies is denoted as $\sum f$ or $N$.

Grouped Frequency Distribution: When the number of observations is large, data is organized into groups called 'Class Intervals' (e.g., $0-10, 10-20$). In the 'Exclusive Method', the upper limit of a class is excluded from that class and included in the next (e.g., the value 10 is counted in $10-20$, not $0-10$).

Class Limits: Each class interval is bounded by two figures. The smaller number is the Lower Class Limit and the larger number is the Upper Class Limit. For example, in the interval $20-30$, $20$ is the lower limit and $30$ is the upper limit.

Class Size and Class Mark: The difference between the upper limit and the lower limit of a class is called the Class Size (or Class Width). The mid-value of a class interval is called the Class Mark, which acts as a representative value for the entire group.

Cumulative Frequency: This is the sum of the frequency of a particular class and all previous classes. A 'Less than' cumulative frequency table tells us how many observations fall below the upper limit of each class, visually represented by adding frequencies from top to bottom.

Range: The difference between the highest and the lowest values in a set of observations is called the Range. It provides a quick visual sense of the spread or dispersion of the data.