3.5.8. Finding class frequency by tally marking

A tally (/) is put against a class for each student whose marks are included in that class. For example, if the marks obtained by a student are 57, we put a tally (/) against class 50–60. If the marks are 71, a tally is put against the class 70–80. If someone obtains 40 marks, a tally is put against the class 40–50.

Tally marking is a simple way to keep track of counts in different categories or classes. When you put a tally for each observation (in this case, each student's score), you're creating a visual representation of the frequency of scores in that class interval. Each tally represents one occurrence, and the tally marks are grouped for ease of counting. For instance, if a student scores 57, you place a tally in the range of 50 to 60. You do this for each student's score to ultimately count how many students fall into each score range.

Think of tally marking like counting votes in an election. Each time a person votes for a candidate, a tally mark is added. After all the votes are collected, you can quickly see how many tallies each candidate has received, just like we do with class scores.

The counting of tally is made easier when four of them are put as //// and the fifth tally is placed across them as /. Tallies are then counted as groups of five. So if there are 16 tallies in a class, we put them as / for the sake of convenience.

The tallying system organizes the counts to make it simpler to tally up large numbers. By grouping every five marks (four vertical lines and one across), the viewer can quickly assess counts without needing to count each line individually. This method prevents confusion and increases speed in counting. So, if a class has 16 tallies, rather than seeing 16 individual lines, you can summarize them more neatly.

Imagine you're counting the number of apples you picked at an orchard. Instead of counting each apple individually in a pile, you create groups of five apples. This grouping allows you to count more quickly and accurately. Once you have your piles, you can easily count how many groups of five you have, making the overall counting process simpler.

While tally marking simplifies raw data making it concise and comprehensible, it does not show the details that are found in raw data. There is a loss of information in classifying raw data though much is gained by summarising it as classified data.

When data is summarized into tallies or frequency distributions, some specific information is inevitably lost. Tally marks show how many items fall into each class but give no detail about the individual observations within those classes. For example, if a class interval for marks is 50-60 and has a frequency of 23, you do not know which specific scores make up that total.

Consider a library's method of organizing books. If they categorize all science fiction books under one label, you know how many there are but you lose the specifics of each title within that category. It makes finding a specific book more challenging without knowing exactly which books belong to that label, just as it can be challenging to know individual scores from a tally.

The frequency of a class is equal to the number of tallies against that class. Therefore, frequency in a class is equal to the number of tallies against that class.

Frequency distribution summarises tally marks into numbers, showing how many observations fall within each class. This process transforms qualitative information (like student scores) into quantitative measures, which makes analyzing and interpreting the data easier. For instance, if there are 10 tallies in the class 50-60, the frequency for that class is recorded as 10.

Imagine a fruit seller at a market who keeps track of the number of oranges sold using tally marks. At the end of the day, they can easily see how many oranges were sold just by counting the tallies rather than trying to remember individual sales. Similarly, frequency distribution provides a clean count for categorizing information and analyzing trends.

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