3.5.7. How should we get the frequency for each class?

In simple terms, frequency of an observation means how many times an observation occurs in the raw data. In our Table 3.1, we observe that the value 40 occurs thrice; 0 and 10 occur only once; 49 occurs five times and so on. Thus the frequency of 40 is 3, 0 is 1, 10 is 1, 49 is 5, and so on.

Frequency is a key concept in statistics that tells us how often a specific value appears in a dataset. This means, if we look at a list of data points (like test scores), frequency lets us count how many times each score appears. For example, if a score of 40 appears three times in the data, we say the frequency of 40 is 3.

Imagine you’re organizing a box of fruit. You have ten apples, five oranges, and two bananas. If you wanted to summarize your fruit collection, you'd say the frequency of apples is 10, oranges is 5, and bananas is 2. This gives you a clear understanding of what you have.

But when the data are grouped into classes as in example 3, the Class Frequency refers to the number of values in a particular class. The counting of class frequency is done by tally marks against the particular class.

When we organize data into classes (like 0-10, 10-20, etc.), we refer to how many scores fall into each range as class frequency. We can use tally marks to keep track. For each score that falls within a range, we make a tally mark. This makes it easy to count at a glance.

Picture a teacher counting the number of students who scored between certain ranges on a math test. For scores between 0 and 10, she marks a tally for each student that falls into that range. This way, she quickly knows how many students scored in that range.

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.

Tally marks are a convenient way to visually summarize frequency data. Each mark (/) represents one observation. When the fifth tally is made, it’s noted as a crossing mark () to help keep the counts organized. For example, if several students scored 57, each would get a tally under the 50-60 class until the total is reached.

Think of a game where you keep score. Each time a player scores, you make a tally on paper. When you reach five scores, you create a crossing line over the four tallies. This method makes it easier to count quickly rather than writing down each score individually.

While it summarizes the 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 summarizing it as classified data.

When we classify data into frequency distributions, we lose some specific details about individual data points. For instance, if we only see that a class contains 10 scores ranging from 50 to 60, we can’t tell which actual scores they were or their unique significance. This loss is an important consideration because while classification makes data easier to analyze, it removes individual nuances.

Consider a box of puzzle pieces; if you separate them by colors into different bags for easier management, you can quickly know how many pieces of each color you have. But if someone later asks you how many of one specific piece type you had, you won't be able to provide that detail. You’ve organized them effectively but at the expense of knowing specifics about their original forms.

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