1. Working out the mean

The times $\displaystyle x_{1},x_{2},x_{3},...,x_{20}$, in minutes, taken by 20 employees to complete a task are summaried by

$\displaystyle \sum(x-50)=140$

using $\displaystyle \overline{x}=\frac{\sum x}{n}$

$\displaystyle \overline{x}=\frac{140}{20}=7$

then add 50 to 7 = 57 is the $\displaystyle \overline{x}$

but in the back of the book, it says 52.8.

Which one is right?

for the 52.8, it uses $\displaystyle \overline{x}=\frac{140}{50}=2.8$

again, Which one is right?

2. Originally Posted by BabyMilo
The times $\displaystyle x_{1},x_{2},x_{3},...,x_{20}$, in minutes, taken by 20 employees to complete a task are summaried by

$\displaystyle \sum(x-50)=140$

using $\displaystyle \overline{x}=\frac{\sum x}{n}$

$\displaystyle \overline{x}=\frac{140}{20}=7$

then add 50 to 7 = 57 is the $\displaystyle \overline{x}$

but in the back of the book, it says 52.8.

Which one is right?

for the 52.8, it uses $\displaystyle \overline{x}=\frac{140}{50}=2.8$

again, Which one is right?

$\displaystyle \sum_{x_i}^{20} ({x_i}-50)=140$

so divide by $\displaystyle 20$:

$\displaystyle \sum_{x_i}^{20} \frac{({x_i}-50)}{20}=7$

or:

$\displaystyle \sum_{x_i}^{20} \left[\frac{x_i}{20}-\frac{50}{20}\right]=7$

which gives:

$\displaystyle \overline{x}-50=7$

or:

$\displaystyle \overline{x}=57$

CB