What is the numerator of the variance equation called?

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BlackTom AI · Accepted Answer

Question restatement: What is the numerator of the variance equation called?

Observation about provided data: The answer options field is empty, so there are no explicit alternative choices to compare. The answer field indicates the intended correct term is 'Sum of squares'.

Reasoning about the concept:
- In both population and sample variance formulas, the numerator is the sum of the squared deviations from the mean. This quantity is commonly referred to as the sum of squares (often abbreviated SS).
- Specifically, for a dataset {x1, x2, ..., xn} with mean x̄, the numerator is ∑(xi − x̄)², which is exactly the sum of squares.
- The denominator then differs by whether you are computing population variance (dividing by n) or sample variance (dividing by n−1). The key distinction is that the numerator is always the sum of squared deviations; the term used to describe that numerator is typically 'sum of squares'.

Why this might be labeled as correct:
- The phrase 'sum of squares' succinctly names the aggregation of squared deviations used as the numerator in both standard forms of the variance. It captures the essence of measuring spread by squaring deviations from the mean and summing them.

Why alternatives (if any were present) might be incorrect:
- If an option claimed the numerator was simply 'squared deviations' without the aggregation term, it could be imprecise; the conventional name is specifically 'sum of squares' because it aggregates all squared deviations into a single scalar.
- If an option referred to the denominator (e.g., 'n' or 'n−1'), it would be incorrect because those terms belong to the denominator, not the numerator.
- If an option suggested 'mean of squared deviations' or 'average of squares', that would describe the variance itself or a related measure (the mean of squared deviations equals the variance only when the sum of squared deviations is divided by n, i.e., the population variance), which would be confusing or incorrect in standard terminology for the numerator.

Note: Since the provided options are absent, this reasoning follows the standard terminology used in variance computations. If options were available, we would map each to this explanation and identify which aligns with the conventional name for the numerator.

PSYCH 3321 SP2025 (28481) Homework 1

What is the numerator of the variance equation called?

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