Data Handling - Recording and Organising Data

Data and Raw Data: Data is a collection of facts or numbers gathered to provide specific information. When data is collected in its original, unorganized form, it is called 'Raw Data'. For example, listing the marks of students exactly as they appear on their answer sheets.

Organization of Data: To make raw data meaningful, it must be organized. This is often done by arranging numbers in an 'Array', which is the arrangement of data in ascending or descending order of magnitude.

Tally Marks: Tally marks are a quick way of keeping track of counts in groups of five. They are represented as vertical lines. For the first four counts, single vertical lines are used ($| | | |$). For the fifth count, a diagonal line is drawn across the previous four lines, looking like a bundle or a gate with a cross-bar. This helps in counting large numbers quickly in sets of 5.

Frequency: The frequency of a particular data value is the number of times that value occurs in the given set of data. For instance, if the number $5$ appears $3$ times in a list, its frequency is $3$.

Frequency Distribution Table: This is a table used to organize data systematically. It typically consists of three columns: the first for the 'Observation' or 'Variable', the second for 'Tally Marks', and the third for 'Frequency' ($f$). It provides a clear visual summary of how the data is distributed.

Range: The range is a measure of the spread of the data. It is the difference between the highest (maximum) value and the lowest (minimum) value in the data set. A larger range indicates more variation in the data.

Arithmetic Mean: The mean (or average) is a single value that represents the center of a data set. It is calculated by adding all the observations together and then dividing that sum by the total number of observations.