Primary School "Average" Question

maninthemirror

New member
Joined
Jan 2, 2016
Messages
4
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 :(
 

Harry_the_cat

Senior Member
Joined
Mar 16, 2016
Messages
1,393
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?
 

Dr.Peterson

Elite Member
Joined
Nov 12, 2017
Messages
4,156
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.
 

JeffM

Elite Member
Joined
Sep 14, 2012
Messages
3,576
If you know some algebra, this is a relatively easy problem. As a pure arithmetic problem, it is a nightmare.

\(\displaystyle c = \text {correct total.}\)

\(\displaystyle i = \text {incorrect total.}\)

\(\displaystyle n = \text {number of items.}\)

\(\displaystyle c - i = 153 - 135.\).......................................edited

\(\displaystyle \dfrac{c}{n} - \dfrac{i}{n} = 129 - 124.5.\)

Can you solve it now?
 
Last edited by a moderator:

maninthemirror

New member
Joined
Jan 2, 2016
Messages
4
What
If you know some algebra, this is a relatively easy problem. As a pure arithmetic problem, it is a nightmare.

\(\displaystyle c = \text {correct total.}\)

\(\displaystyle i = \text {incorrect total.}\)

\(\displaystyle n = \text {number of items.}\)

\(\displaystyle c - f = 153 - 135.\)

\(\displaystyle \dfrac{c}{n} - \dfrac{i}{n} = 129 - 124.5.\)

Can you solve it now?
What is f?
 

JeffM

Elite Member
Joined
Sep 14, 2012
Messages
3,576
Oops. That f should be i. Sorry.
 

Harry_the_cat

Senior Member
Joined
Mar 16, 2016
Messages
1,393
Yes I was assuming no algebra was involved.
 
Top