Question

what is the purpose of squaring deviations when calculating variance?
a. to express deviations in absolute values
b. to eliminate large numbers
c. to emphasize smaller deviations
d. to eliminate negative values and emphasize larger differences

Explanation:

• Option a: Expressing in absolute values is done by taking absolute value, not squaring. So a is wrong.
• Option b: Squaring can increase large numbers (e.g., squaring 10 gives 100), so it doesn't eliminate large numbers. b is wrong.
• Option c: Squaring emphasizes larger deviations (e.g., deviation of 3 squared is 9, deviation of 2 squared is 4), not smaller ones. c is wrong.
• Option d: Deviations from the mean can be negative. Squaring them makes all values non - negative (eliminates negative values). Also, larger deviations, when squared, become relatively larger (e.g., 5 - mean = 3, (- 4)-mean=-4; 3² = 9, (-4)² = 16), so it emphasizes larger differences. So d is correct.

Answer:

d. To eliminate negative values and emphasize larger differences