3.5.6. Adjustment in Class Interval

A close observation of the Inclusive Method in Table 3.4 would show that though the variable “income” is a continuous variable, no such continuity is maintained when the classes are made. We find “gap” or discontinuity between the upper limit of a class and the lower limit of the next class. For example, between the upper limit of the first class: 899 and the lower limit of the second class: 900, we find a gap of 1.

In a frequency distribution, when we categorize data into classes, we might create gaps between the classes if they are not adjusted properly. For example, if one class ends at 899 and the next begins at 900, there's a gap of 1 unit. This lack of continuity can misrepresent the data, particularly if we are dealing with continuous variables like income.

Think of it as sorting people into height categories: if one group ends at 150 cm and the next starts at 151 cm, you have a gap. But if we adjust the groups to overlap slightly (say, 150 cm to 151 cm), we have a smoother transition. This overlap makes it easier to understand how many people fall within that range.

To ensure the continuity of the variable while classifying data, this is achieved by making an adjustment in the class interval. The adjustment is done in the following way: 1. Find the difference between the lower limit of the second class and the upper limit of the first class. For example, in Table 3.4 the lower limit of the second class is 900 and that the upper limit of the first class is 899. The difference between them is 1, i.e. (900 – 899 = 1) 2. Divide the difference obtained in (1) by two i.e. (1/2 = 0.5) 3. Subtract the value obtained in (2) from lower limits of all classes (lower class limit – 0.5) 4. Add the value obtained in (2) to upper limits of all classes (upper class limit + 0.5).

Adjusting class intervals ensures there are no gaps between classes. First, we check the gap length; if the next class starts at 900 and the previous class ends at 899, the gap is 1 unit. We then halve this gap (to 0.5) and adjust all class boundaries. So, we reduce 0.5 from each lower limit and add 0.5 to each upper limit. This way, the classes overlap slightly, eliminating gaps.

Imagine you are organizing your books. If one shelf ends at a certain height and the next shelf starts way above that, it looks awkward. Instead, by making the shelves overlap slightly, books can be placed neatly, and finding a particular book becomes easier. This is similar to adjusting our class intervals.

After the adjustments in class limits, the equality (1) that determines the class mark would be modified as follows: Adjusted Class Mark = (Adjusted Upper Class Limit + Adjusted Lower Class Limit)/2.

After adjusting the class intervals, we re-calculate the class mark. The class mark is the midpoint of each class, and by adjusting the limits, we ensure that the class marks now accurately represent the values in those classes without leaving out any data. The adjusted class mark is simply the average of the newly adjusted lower and upper limits.

Think about a scale where you've marked the middle point for weights. If you shift your scale up or down, that middle point has to be recalculated to ensure it's still accurately reflecting the average of what's on your scale. This allows for a more precise and usable measurement.

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