Primary School "Average" Question

maninthemirror

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Pamela found the average of some numbers to be 124.5. She realized that she had keyed in one number wrongly. Instead of keying in 153, she keyed in 135. The actual average was 129. How many numbers were there?

Please help. Need help desperately as my submission is tmr :(
 
How much bigger was the number she keyed in compared to the number she should have keyed in? What effect did this have on the average?
 
Pamela found the average of some numbers to be 124.5. She realized that she had keyed in one number wrongly. Instead of keying in 153, she keyed in 135. The actual average was 129. How many numbers were there?

Please help. Need help desperately as my submission is tmr :(
This can be solved more easily (in the sense of needing less special thinking) by a little algebra. Have you (or the student) learned any?

On the other hand, Harry's approach uses number sense well. Since the sum of the numbers is divided by n, anything you add to that sum (in making a correction, for example) is also divided by n.
 
If you know some algebra, this is a relatively easy problem. As a pure arithmetic problem, it is a nightmare.

[MATH]c = \text {correct total.}[/MATH]
[MATH]i = \text {incorrect total.}[/MATH]
[MATH]n = \text {number of items.}[/MATH]
[MATH]c - i = 153 - 135.[/MATH].......................................edited

[MATH]\dfrac{c}{n} - \dfrac{i}{n} = 129 - 124.5.[/MATH]
Can you solve it now?
 
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What
If you know some algebra, this is a relatively easy problem. As a pure arithmetic problem, it is a nightmare.

[MATH]c = \text {correct total.}[/MATH]
[MATH]i = \text {incorrect total.}[/MATH]
[MATH]n = \text {number of items.}[/MATH]
[MATH]c - f = 153 - 135.[/MATH]
[MATH]\dfrac{c}{n} - \dfrac{i}{n} = 129 - 124.5.[/MATH]
Can you solve it now?

What is f?
 
It is good that you got it!

Here is how I would do this problem.

Lets us suppose that there are n numbers and their average is 124.5.

Now there is an error where the total number should have been 18 more causing the average to become 129.

So the extra 18 caused the average to go up 4.5 points. Now 18/n =4.5 or 18/4.5 = n. That is n =4.


Another way of thinking about it is that in effect each of the n numbers went up by 4.5 and the sum of the extra numbers is 18. That is 4.5*n = 18 or 18/4.5 = n.
 
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