What is a frequency distribution table and how are its columns (class interval, frequency, tally, class boundary) defined and calculated?

Here's an explanation of each column in the table:

1. Class interval: These are the ranges into which the data is grouped. For example, "2-3" includes all data points from 2 up to and including 3.
2. Frequency: This is the number of data points that fall within each specific class interval.
3. Tally: This column uses marks to count the frequency for each class interval. Each vertical line represents one data point, and a diagonal line across four vertical lines completes a group of five.
4. Class boundary: These are the true limits of each class interval, used to ensure there are no gaps between consecutive classes, which is important for creating continuous graphs like histograms.

To calculate the class boundaries, you typically find the midpoint between the upper limit of one class and the lower limit of the next. In this table, there's a gap of 1 between the upper limit of one class and the lower limit of the next (e.g., 4 - 3 = 1). So, we add and subtract half of this gap (0.5) to the class limits.

Let's correct the class boundaries shown in the table:

• For class interval 2-3: Lower boundary = 2 - 0.5 = 1.5 Upper boundary = 3 + 0.5 = 3.5 Class boundary: 1.5-3.5 (This is correct in the table)

• For class interval 4-5: Lower boundary = 4 - 0.5 = 3.5 Upper boundary = 5 + 0.5 = 5.5 Class boundary: 3.5-5.5 (This is correct in the table)

• For class interval 6-7: Lower boundary = 6 - 0.5 = 5.5 Upper boundary = 7 + 0.5 = 7.5 Class boundary: 5.5-7.5 (The table incorrectly shows 5.5-9.5)

• For class interval 8-9: Lower boundary = 8 - 0.5 = 7.5 Upper boundary = 9 + 0.5 = 9.5 Class boundary: 7.5-9.5 (The table incorrectly shows 9.5-11.5)

• For class interval 10-11: Lower boundary = 10 - 0.5 = 9.5 Upper boundary = 11 + 0.5 = 11.5 Class boundary: 9.5-11.5 (The table incorrectly shows 11.5-13.5)

• For class interval 12-13: Lower boundary = 12 - 0.5 = 11.5 Upper boundary = 13 + 0.5 = 13.5 Class boundary: 11.5-13.5 (The table incorrectly shows 13.5-15.5)