To calculate the standard deviation of a frequency distribution using the direct method, follow these steps:

Given dataTo calculate the standard deviation of a frequency distribution using the direct method, follow these steps:

Given

• Sizes ($X$): $4, 5, 6, 7, 8, 9, 10$
• Frequencies ($f$): $6, 12, 15, 28, 20, 14, 5$

Step 1: Calculate the mean ($\bar{X}$)

The formula for the mean is:

$\bar{X} = \frac{\sum fX}{\sum f}$

Where:

[ \sum fX = (4 \times 6) + (5 \times 12) + (6 \times 15) + (7 \times 28) + (8 \times 20) + (9 \times 14) + (10