True. The sum of deviations from the mean is always zero.

The mean is the average of a set of numbers. Deviations are the differences between each number in the set and the mean. When you add up all of these differences, the positive and negative deviations cancel each other out, resulting in a sum of zero.

This property can be mathematically proven:

Let X₁, X₂, ..., X_n be a set of n numbers. The mean (μ) is calculated as:

μ = (X₁ + X₂ + ... + X_n) / n

The deviation of each number from the mean is (X_i - μ). The sum of these deviations is:

Σ(X_i - μ) = (X₁ - μ) + (X₂ - μ) + ... + (X_n - μ)

Σ(X_i - μ) = (X₁ + X₂ + ... + X_n) - nμ

Since μ = (X₁ + X₂ + ... + X_n) / n, then nμ = (X₁ + X₂ + ... + X_n)

Σ(X_i - μ) = (X₁ + X₂ + ... + X_n) - (X₁ + X₂ + ... + X_n) = 0

Therefore, the sum of deviations from the mean is always zero.

See this math explanation, or this article explaining the topic.