MHB Average Problem [Need Formula]

[zidan3311]

hi all..

how to make formula for problem below :

The average math test scores of 36 students is 86. There are four students attend subsequent replications and obtain an average value of 80. Find the average value of all the students!

can you make simple?

zidan3311

 

[SuperSonic4]

What do you know about the average and how it's worked out?

Could you find the total sum for the 36 students using the average given and the fact there are 36 students in the sample size?

 

[MarkFL]

You could use what's called a weighted average here. Suppose you have $n$ groups, and each group has a mean of $\overline{x_i}$ and $m_i$ members. Then the mean $\overline{x}$ of all groups combined is given by:

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Weighted Average​

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$$\overline{x}=\frac{\sum\limits_{i=1}^{n}\left(m_i\cdot\overline{x_i}\right)}{\sum\limits_{i=1}^{n}\left(m_i\right)}\tag{1}$$[/box]

In your case, you have 2 groups ($n=2$), where:

$$m_1=36,\,\overline{x_1}=86,\,m_2=4,\,\overline{x_2}=80$$

And so what do you get when you apply this data to (1)?