The correct one is: If the weight of -2 is decreased to 1 and the weight of 1 is decreased to 3, the weighted average would decrease.
What statement is true?
The weighted average of a set of values is calculated by multiplying each value by its respective weight, summing these products, and then dividing by the sum of the weights.
Given the number line:
-3 -2 -1 0 1 2 3
2 6 + -3 -2 2 3
To calculate the weighted average, use the following formula:
Weighted Average = (Sum of (Values * Weights)) / (Sum of Weights)
Let's calculate the weighted average:
Weighted Average = ((2 * 6) + (-3 * 2) + (-2 * 1) + (1 * 3)) / (6 + 2 + 1 + 3) = (12 - 6 - 2 + 3) / 12 = 7 / 12 ≈ 0.58
Now, let's analyze the statements:
The weighted average is approximately 0.58, not -0.5, so the first statement is incorrect.
If the weight of -2 is increased, this would increase its contribution to the weighted average, potentially increasing the weighted average.
If the weight of 1 is increased, this would also increase its contribution to the weighted average, potentially increasing the weighted average.
Decreasing the weight of -2 to 1 and decreasing the weight of 1 to 3 would reduce the contribution of -2 and increase the contribution of 1, which might decrease the weighted average.
So, among the provided options, the correct one is: If the weight of -2 is decreased to 1 and the weight of 1 is decreased to 3, the weighted average would decrease.