Question

The average resulting from the multiplication of each value by a weighted factor is known as .

Answer 1

Weighted average is the average resulting from the multiplication of each value by a weighted factor. It is calculated as,

$\text{Weighted Average}=\frac{(w_1\times n_1)+(w_2\times n_2)+\dots +(w_l\times n_l)}{w_1+w_2+\dots +w_l}$,

where $w_1,w_2,\dots ,w_l$ are weighted factors and $n_1,n_2,\dots ,n_l$ are data points.

For example, let the average age of $20$ cows is $6$ years and the average age of $10$ goats is $4$ years.

This can be represented as,


Here, the number of cows $(w_1=20)$ and the number of goats $(w_2=10)$ are weighted factors and their average age, $n_1=6$ and $n_2=4$ are the data points.

Thus, their weighted average age will be calculated as,

$\begin{array}{cc}\text{Weighted Average age}& =\frac{(w_1\times n_1)+(w_2\times n_2)}{w_1+w_2}\\ & =\frac{(20\times 6)+(10\times 4)}{20+10}\\ & =\frac{120+40}{30}\\ & =\frac{160}{30}\\ & =5.33\end{array}$

Thus, the weighted average age of these animals is $5.33$ years.