Question

③ the weight of point f is ¼ the weight of point g. find the weighted average.

Explanation:

1. Let the weight of point \(G\) be \(w_G = 4\) and the weight of point \(F\) be \(w_F=1\) (since the weight of point \(F\) is \(\frac{1}{4}\) the weight of point \(G\)).

• From the number - line, the value of point \(F\) is \(x_F=- 2\) and the value of point \(G\) is \(x_G = 5\).

1. Recall the formula for the weighted average:

• The formula for the weighted average \(\bar{x}=\frac{\sum_{i = 1}^{n}w_ix_i}{w_1 + w_2+\cdots+w_n}\). In our case, with two points \(F\) and \(G\), \(\bar{x}=\frac{w_Fx_F+w_Gx_G}{w_F + w_G}\).
• Substitute \(w_F = 1\), \(x_F=-2\), \(w_G = 4\), and \(x_G = 5\) into the formula:
• First, calculate the numerator: \(w_Fx_F+w_Gx_G=1\times(-2)+4\times5=-2 + 20=18\).
• Then, calculate the denominator: \(w_F + w_G=1 + 4=5\).

1. Calculate the weighted average:

• \(\bar{x}=\frac{18}{5}=3.6\).

Step1: Define weights and values

Let \(w_F = 1\), \(x_F=-2\), \(w_G = 4\), \(x_G = 5\).

Step2: Calculate numerator of weighted - average formula

\(w_Fx_F+w_Gx_G=1\times(-2)+4\times5=-2 + 20 = 18\)

Step3: Calculate denominator of weighted - average formula

\(w_F + w_G=1 + 4=5\)

Step4: Calculate weighted average

\(\bar{x}=\frac{18}{5}=3.6\)

Answer:

\(3.6\)