Question:

The pirce of a CD is denoted by $x. For 60CDs bought in different stores it is found that $\displaystyle \sum(x-12) = 53.60$. 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:

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

$\displaystyle 60\times12+53.40 = 773.40$

$\displaystyle \sum\bar{x} = 773.40$

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

Mean of 100 CDs = $\displaystyle \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?