Find the mean() of the first ten prime numbers and hence show that 10i=1(xiâˆ ) = 0 - Maths - Statistics

Question

Find the mean()
of the first ten prime numbers and hence show that
 10 i =1 (
xi âˆ’ 
 ) = 0

Rayya Halim · Accepted Answer

Mean of Fist ten prime numbers = (2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29) / 10

= 12.9

assume $\bar{x}$ stands for average of $x_{i}$ numbers i = 1 to n.

Proceed as follows

$\bar{x} = \frac{\sum_{i = 1}^{n} x_{i}}{n} \Rightarrow n \times \bar{x} = \frac{\sum_{i = 1}^{n} x_{i}}{n} \Rightarrow \frac{\sum_{i = 1}^{n} x_{i}}{n} - n \bar{x} = 0 \Rightarrow \frac{\sum_{i = 1}^{n} x_{i}}{n} - \sum_{i = 1}^{n} \bar{x} = 0 \Rightarrow \sum_{i = 1}^{n} (x_{i} - \bar{x}) = 0$

Find the mean() of the first ten prime numbers and hence show that 10 i =1 ( xi − ) = 0

Find the mean( $bar{x} !,$ ) of the first ten prime numbers and hence show that

10 i =1 ( xi − $bar{x} !,$ ) = 0