Question

Explain why a weighted average is used instead of an arithmetic average.

a) Weighted averages give equal importance to all values.
b) Weighted averages account for the influence of outliers.
c) Weighted averages allow for more flexibility in calculations.
d) Weighted averages consider the relative significance of each value.

Answer 1

A weighted average is used instead of an arithmetic average because it considers the relative significance of each value and accounts for the influence of outliers.

Step-by-step explanation:

A weighted average is used instead of an arithmetic average because it considers the relative significance of each value. In a weighted average, different values are given different weights based on their importance or influence. This allows for more accurate calculations by giving more importance to values that have a greater impact on the overall average.

For example, if you are calculating the average grade of a student, you may assign a higher weight to the final exam grade compared to the homework grades because it carries more significance in determining the overall performance.

Weighted averages also account for the influence of outliers by assigning lower weights to their values. This helps to reduce the impact of extreme values that could potentially skew the arithmetic average.