gettinit wrote:
Karishma can you please explain your method a bit more? I don't understand how you solved the problem using it? thanks
What is weighted average?
It is average when each value has a different weight. e.g. a group of friends has 10 boys and 20 girls. Average age of boys is 20 years and average age of girls is 17 years. What is the average age of the group?
Here, the average is weighted since we have different number of boys and girls.
We calculate it as follows:
\(W Avg = \frac{20*10 + 17* 20}{10 + 20}\)
What we are doing instinctively here is using weighted average formula which as given below:
\(C_{avg} = \frac{C_1*W_1 + C_2 * W_2}{W_1 + W_2}\)
You need to find the average of C and W is the weight. In the example above, C is age and W is number of boys and girls.
The alligation method, or the scale method as we call it, is based on the weighted averages formula itself:
\(C_{avg} = \frac{C_1*W_1 + C_2 * W_2}{W_1 + W_2}\)
If I re-arrange the formula, I get
\(\frac{W_1}{W_2} = \frac{C_2 - C_{avg}}{C_{avg} - C_1}\)
So I get that weights will be in the same ratio as difference between higher value of C and average value of C and difference between average value of C and lower value of C.
How does this help? Knowing this, we can directly make a diagram and get the answer.
e.g. A group of friends has 10 boys and some girls. Average age of boys is 20 years and average age of girls is 17 years. The average age of the group is 18 years. How many girls are there?
Draw:
Attachment:
Ques1.jpg
On a scale (number line), mark 17 years as age of girls, 18 years as average and 20 years as age of boys. Now, distance between 17 and 18 is 1 and distance between 18 and 20 is 2, The ratio of W1/W2 will be 2:1 (Note, the numbers 1 and 2, give a ratio of 2:1 for girls:boys as seen by the formula)
Since there are 10 boys, there will be 20 girls.
This method is especially useful when you have the average and need to find the ratio of weights.
Karishma, this was very helpful and your way of doing the scale method makes sense because
doesn't explain it clearly in the foundation book. My only question is your equation
How did you re-arrange the formula to get that? I don't see it. Thanks in advance!