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The times taken to produce each of the first 4 batches of a new product were as follows
Batch no. Time taken
1 100 minutes
2 70 minutes
3 59 minutes
4 55 minutesWhat was the rate of learning closest to? (1 d.p)
The answer I got is 85%. I didn’t quite get how they have arrived into 84.3%.Pls tell me how to find the answer
The average time per batch to produce 4 batches is (100 + 80 + 50 + 55) / 4 = 71.25 minutes.
Since producing 4 batches involves doubling 2 times, the learning rate is the square root of 71.25/100 = 0.843 (or 84.3%)
Have you not watched my free lectures on this? The lectures are a complete free course for Paper F5 and cover everything needed to be able to pass the exam well.
Btw , sir u made a mistake by putting wrong values in the place of 70 and 59 minutes. And when I took the square root of that number the answer which I’m getting is 91% . I’m so confused
You are right – I copied the numbers wrongly (although the different is tiny).
I should have written (100 + 70 + 59 + 55) / 4 = 71.
Therefore the learning rate = sq root of 71/100 = sq root of 0.71 = 0.843 (or 84.3%).
I have no idea why you are getting 91% – you must be pressing the wrong button on your calculator.
Ok .I understood that method. But as per the rule I can also calculate by dividing 71 by 85 ( ie avg time for 4 batches / avg time for 2 batches ) and get the learning rate. By doing in this way now I’m getting 83.5%. can I do in this method too? Is my answer correct?
Your arithmetic is correct, but it would be the wrong answer for the exam.
The reason is that in real life it would be a miracle if the learning rate was to stay constant – especially at the very beginning (and over these 4 batches it is not constant). So the longer the period we look over then the better our estimate of the average rate of learning will be.
So in the exam, if they give you 4 batches as here, you must compare the average for 4 with the first; if they gave you 8 batches then you must compare the average for 8 with the first (and then take the third root), and so on.
(You can only be asked to estimate the learning rate when it is doubling)
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