What is the abbreviation for the total of squared deviations?

What is the abbreviation for the total of squared deviations?

• A. Sum of Squares (SS)
• B. Variance
• C. Standard Deviation
• D. Range

Answer: (A)

The total of squared deviations is the sum of squared distances from the mean, written as sum of (xi − x̄)². This quantity is abbreviated SS, standing for Sum of Squares. It captures the overall dispersion by adding up how far each data point is from the mean after squaring those differences. Why this is the best answer: SS specifically refers to this total, while the other terms denote different things. Variance is the average of those squared deviations (SS divided by n or n−1, depending on population or sample). Standard deviation is the square root of that average. Range is simply the difference between the maximum and minimum values. So SS is the correct abbreviation for the total of squared deviations. Example: data 2, 4, 6 have mean 4. Squared deviations are 4, 0, 4; their sum is 8, so the sum of squares is 8. Variance would be 8/3 and standard deviation would be sqrt(8/3), illustrating how SS differs from the other measures.

The total of squared deviations is the sum of squared distances from the mean, written as sum of (xi − x̄)². This quantity is abbreviated SS, standing for Sum of Squares. It captures the overall dispersion by adding up how far each data point is from the mean after squaring those differences.

Why this is the best answer: SS specifically refers to this total, while the other terms denote different things. Variance is the average of those squared deviations (SS divided by n or n−1, depending on population or sample). Standard deviation is the square root of that average. Range is simply the difference between the maximum and minimum values. So SS is the correct abbreviation for the total of squared deviations.

Example: data 2, 4, 6 have mean 4. Squared deviations are 4, 0, 4; their sum is 8, so the sum of squares is 8. Variance would be 8/3 and standard deviation would be sqrt(8/3), illustrating how SS differs from the other measures.