The average of 10 consecutive even numbers is 25. If the even number just preceding the smallest of the 10 given numbers is also included, then what will be the new average?

The average of 10 consecutive even numbers is 25.

Sum of the 10 consecutive even numbers = $$25\times10$$ = 250

Let's assume the smallest even number of this sequence is 'y'.

y+(y+2)+(y+4)+(y+6)+(y+8)+(y+10)+(y+12)+(y+14)+(y+16)+(y+18) = 250

10y+2+4+6+8+10+12+14+16+18 = 250

10y+90 = 250

10y = 250-90

10y = 160

y = 16

If the even number just preceding the smallest of the 10 given numbers is also included,

So the even number just preceding the smallest of the 10 given numbers = (16-2) = 14

new average = $$\frac{sum\ of\ ten\ numbers+new\ number\ in\ the\ sequence}{number\ of\ data}$$

$$\frac{250+14}{10+1}$$

= $$\frac{264}{11}$$

= 24