1.11.1.4. Inclusive Method

In this method, a value equal to the upper limit of a group is included in the same group. Therefore, it is known as inclusive method. Classes are mentioned in a different form in this method, as shown in the first column of Table 1.7.

The inclusive method is a way of grouping data where both the upper and lower limits of a group are considered part of that group. For instance, if we have a group labeled as 50 to 59, this means that any value from 50 to 59, including both 50 and 59, counts in this group. This is different from the exclusive method where the upper limit is not counted in the same group.

Imagine you're playing a game where players are grouped based on scores. If the score range is 30-39 in an exclusive method, then a player who scores 39 would not be included. In an inclusive method, that player gets counted in the 30-39 range, meaning they are included in the group.

Table 1.7 shows the frequency distribution using the inclusive method: Group f Cf 0 – 9 4 4 10 – 19 5 9 20 – 29 5 14 30 – 39 7 21 40 – 49 6 27 50 – 59 10 37 60 – 69 8 45 70 – 79 6 51 80 – 89 5 56 90 – 99 4 60.

In Table 1.7, each group represents a range of values, while 'f' stands for frequency, which indicates how many times values fall within each range. 'Cf' represents cumulative frequency, which adds up all frequencies up to that group. For example, in the group 30 to 39, there are 7 instances, and when added to the previous groups, the cumulative frequency becomes 21.

Think of it like counting the number of students who scored within specific ranges on a test. The first group would capture scores ranging from 0 to 9. If four students scored between 0 to 9, your frequency is 4. When you reach the next group, which might be 10 to 19, and find five more students, your total (cumulative frequency) up to this point would be 9.

A graph of frequency distribution is known as the frequency polygon. It helps in comparing two or more than two frequency distributions. The two frequencies are shown using a bar diagram and a line graph respectively.

A frequency polygon is a graphical representation of the frequencies of different groups. It’s created by plotting points for each group’s frequency and connecting them with lines, providing a clear visual representation of data. Using bars for one set of data and a line graph for another allows for easy comparison.

Imagine you're looking at two different bar charts, one showing student performance in Math and the other in Science. By drawing a line over the math scores, you can visually compare how students performed in each subject at a glance. The line tells you quickly which subject had generally higher scores.

When the frequencies are added they are called cumulative frequencies and are listed in a table called cumulative frequency table. The curve obtained by plotting cumulative frequencies is called an Ogive.

An Ogive is a curve that represents cumulative frequency. It helps to show how many values fall below a particular threshold. In the less-than Ogive, we plot the cumulative frequencies starting from the upper limit of each class. This method results in an upward-sloping curve, illustrating the accumulation of frequencies.

Think of an Ogive like counting how many books you've read over the years. At first, you count a few books, but as time goes on, you add more and more to your count. As you plot this on a graph, it would show an upward trend, visually representing your reading journey.

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