Data Handling - Tally Marks

Data is a collection of information, such as numbers, words, measurements, or observations, gathered to provide insights. In data handling, we organize this information systematically to make it easier to understand.

Tally marks are a method used to record and count data quickly. Instead of writing numbers repeatedly, we use vertical strokes to keep track of frequencies in groups of five.

For the first four counts, we use simple vertical lines. One is represented as $|$, two as $||$, three as $|||$, and four as $||||$. Each stroke represents a single unit of data.

To represent the number $5$, we do not add a fifth vertical line. Instead, we draw a diagonal line across the first four vertical lines. This creates a visual 'bundle' or 'gate' $(\cancel{||||})$ that represents exactly $5$ units.

Numbers greater than $5$ are shown as a combination of groups of five and individual strokes. For example, the number $8$ is represented as one bundle of five followed by three separate vertical lines $(\cancel{||||} \ |||)$.

A Frequency Table is a structured way to present data. It typically consists of three columns: the Category (the item being counted), the Tally Marks (the strokes), and the Frequency (the total numerical count).

The Frequency ($f$) is the total number of times a particular value or item occurs in the data set. Summing up all the frequencies gives the total number of observations recorded.

Tally marks make counting large data sets more efficient because they allow us to 'skip-count' by fives $(\text{e.g., } 5, 10, 15, \dots)$ rather than counting every single item one by one.