$\frac{∑f(x-x̄)}{N}$ Is a formula used to calculate for ____________

Analyze the question: The expression Σf(x − x̄)/N is a statistical measure of dispersion (spread) for grouped data. We need to identify which measure it represents.

Concept: measures of dispersion for grouped data

• Mean deviation: MD = Σf|x − x̄| / N. It takes the absolute value of each deviation from the mean.
• Variance: σ² = Σf(x − x̄)² / N. It squares each deviation.
• Standard deviation: σ = √[Σf(x − x̄)² / N]. It is the square root of the variance.
• Quartile: This is a position measure that divides the data into four parts, so it does not use this formula.

Solution:

1. The formula has no square, so it is not the variance, and it has no square root, so it is not the standard deviation.
2. It is not a quartile, because quartiles come from cumulative frequency and position, not from deviations from the mean.
3. The only measure left that is built from deviations from the mean, without squaring them, is the mean deviation.

A note on the formula as written: Strictly, the mean deviation uses absolute values, |x − x̄|. Without the absolute value signs, Σf(x − x̄) always equals zero, because positive and negative deviations cancel out. The question most likely omitted the modulus bars by a typesetting slip.

Answer: D. Mean deviation

Tip: Remember the pattern:

• Single deviation with absolute value → mean deviation
• Squared deviation → variance
• Square root of the squared deviation → standard deviation

If you see no square and no root, think "mean deviation."