Question

what is the average of the points a, b and c with weights 3, 1 and 4 respectively?

Explanation:

Step1: Identify the coordinates

From the graph, assume the points are one - dimensional (on the y - axis as no x - coordinates are relevant for this average calculation). Let \(A=- 3\), \(B = 3\), \(C=2\).

Step2: Apply the weighted - average formula

The weighted - average formula is \(\bar{x}=\frac{w_1x_1 + w_2x_2+w_3x_3}{w_1 + w_2+w_3}\), where \(w_1 = 3\), \(x_1=-3\), \(w_2 = 1\), \(x_2 = 3\), \(w_3 = 4\), \(x_3=2\).
First, calculate the numerator: \(w_1x_1+w_2x_2 + w_3x_3=3\times(-3)+1\times3 + 4\times2=-9 + 3+8=2\).
Then, calculate the denominator: \(w_1 + w_2+w_3=3 + 1+4=8\).
So, the weighted average \(\bar{x}=\frac{2}{8}=\frac{1}{4}=0.25\).

Answer:

\(0.25\)