\( \bar{X}=\frac{\sum f x}{N} \) \( \mathrm{x}= \) Midpoint \( \mathrm{f}= \) frequency

The formula you've shared is a foundational concept in statistics, specifically in the calculation of the mean for grouped data. In this context, the midpoint (\( \mathrm{x} \)) represents the average of the upper and lower bounds of a class interval, effectively yielding a single representative value for each class. The frequencies (\( \mathrm{f} \)), on the other hand, indicate how many observations fall within each interval, allowing statisticians to weigh the midpoints correctly when calculating the overall mean. When applying this formula, a common mistake is neglecting to properly determine the midpoints for each interval, leading to inaccurate results. Additionally, ensure your total frequency (\( N \)) is correct; if the sum of the frequencies doesn’t match the number of observations, your mean will be off! Double-checking these calculations can save you from unnecessary headaches down the line.