MHB Question about Averages (Kizzy Reem's Question on Facebook)

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To find the new mean average for 25 students after adding a student who scored 67%, the total marks for the original 24 students, with a mean of 78%, is calculated as 78 times 24. The formula for the new mean involves adding the 67% score to this total and dividing by 25. The calculation shows how to derive the new average using these values. This method effectively updates the mean by incorporating the additional student's score. The discussion provides a clear mathematical approach to solving the problem.
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Kizzy Reem on Facebook writes:

If the mean average for 24 students is 78% and another student got 67% what is the mean average for the 25 students?
 
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Sudharaka said:
Kizzy Reem on Facebook writes:

If the mean average for 24 students is 78% and another student got 67% what is the mean average for the 25 students?

Hi Kizzy, :)

Let \(x_{i}\) be the marks of the \(i^{th}\) student. Then the mean value of marks for 24 students is,

\[M_{24}=\frac{1}{24}\sum^{24}_{i=1} x_{i}=78\]

\[\Rightarrow \sum^{24}_{i=1} x_{i}=78\times 24~~~~~~~~~~(1)\]

Since the 25th student got 67% marks,

\[M_{25}=\frac{1}{25}\left(67+\sum^{24}_{i=1} x_{i}\right)~~~~~~~~(2)\]

Using (1) and (2) you'll be able to calculate \(M_{25}\). :)
 
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