Question

What is the average of the points \[\blue{a}\], \[\pink{b}\] and \[\green{c}\] with weights \[\blue{2}\], \[\pink{4}\] and \[\green{1}\] respectively?

Answer 1

The weighted average of points blue a, pink b, and green c with weights blue 2, pink 4, and green 1 respectively is calculated using the formula for weighted average. This yields a value equal to
`\(\frac{{2 * \blue{a} + 4 * \pink{b} + 1 * \green{c}}}{{2 + 4 + 1}}\)`.

Step-by-step explanation:

To determine the weighted average, multiply each point by its respective weight and then sum these products. In this scenario, multiply blue a, pink b, by 4, and green c by 1, then add these results together. Next, sum the weights (2 + 4 + 1) to use as the denominator in the weighted average formula. Finally, divide the total sum of the weighted values by the sum of the weights to obtain the weighted average. This method takes into account the importance or significance of each point by assigning different weights to them.

For instance, if blue a, pink b, and green c represent numerical values such as 10, 20, and 30 respectively, and their corresponding weights are 2, 4, and 1, the calculation would be
`\(\frac{{2 * 10 + 4 * 20 + 1 * 30}}{{2 + 4 + 1}} = \frac{{20 + 80 + 30}}{{7}} = \frac{{130}}{{7}}\)`. Therefore, the weighted average would be
`\(\frac{{130}}{{7}}\)` units. This method helps compute an average that accounts for the significance of each point based on their respective weights.