# Math Help - Mean Help!

1. ## Mean Help!

Question:
The pirce of a CD is denoted by $x. For 60CDs bought in different stores it is found that $\sum(x-12) = 53.60$. Calculate the mean price of these CDs. The mean price of a further 40 CDs is found to be$11.64. The mean price of the 100 CDs.

Attempt:
$\sum^{60}_{i=1}(x-12) = 53.40$

$60\times12+53.40 = 773.40$

$\sum\bar{x} = 773.40$

$\bar{x} = \frac{773.40}{60} = \12.89$

Mean of 100 CDs = $\frac{12.89 + 11.64}{2} = \12.27$

The mean for 60 CDs is correct! but for 100 CDs is wrong. Where did I do wrong?

2. Originally Posted by looi76

Mean of 100 CDs = $\frac{12.89 + 11.64}{2} = \12.27$

The mean for 60 CDs is correct! but for 100 CDs is wrong. Where did I do wrong?
You need to take a weighted average of the two means like so:

$\bar{x}_{100} = \frac{60*\bar{x}_{60}+40*\bar{x}_{40}}{100}$