Working out the mean

BabyMilo · #1 $Old$ November 15th, 2009, 09:19 AM

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

$\sum(x-50)=140$

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

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

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

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

Which one is right?

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

then add 50.

again, Which one is right?

thanks for your help!

CaptainBlack · #2 $Old$ November 20th, 2009, 11:05 AM

Quote:

Originally Posted by BabyMilo $View Post$

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

$\sum(x-50)=140$

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

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

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

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

Which one is right?

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

then add 50.

again, Which one is right?

thanks for your help!

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

so divide by $20$ :

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

or:

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

which gives:

$\overline{x}-50=7$

or:

$\overline{x}=57$

CB