Here is total $$50$$ numbers, so $$N=50$$

Variance $$ = $$ $${{\sum {{x^2}} } \over {50}} - {\left( {{{\sum x } \over {50}}} \right)^2}$$

Here $$\sum {{x^2}} = $$ sum of square of first $$50$$ even natural number.

$$ = {2^2} + {4^2} + ..... + {100^2}$$

$$ = {2^2}\left[ {{1^2} + {2^2} + ....... + {{50}^2}} \right]$$

$$ = 4\left[ {{{50 \times 51 \times 101} \over 6}} \right]$$

So, $${{\sum {{x^2}} } \over {50}} = {{4 \times 51 \times 101} \over 6} = 3434$$

$$\sum {x = } $$ sum of first $$50$$ even natural numbers

$$ = 2 + 4 + ...... + 100$$

$$ = 2\left[ {1 + 2 + .... + 50} \right]$$

$$ = 2\left[ {{{50 \times 51} \over 2}} \right]$$

$$ = 50 \times 51$$

$$\therefore\,\,\,$$ $${\left( {{{\sum x } \over {50}}} \right)^2} = {\left( {{{50 \times 51} \over {50}}} \right)^2} = 2601$$

$$\therefore\,\,\,$$ Variance $$ = 3434 - 2601$$ $$=833$$