The means of two groups of 15 and 20 observations are 20 and 25 respectively. Find the mean of all the 35 observations.

 See

i) group is 15 it's mean is 20

so the total sum will be 15 * 20 = 300

Now

ii) group is 20 it's mean is 25

so the total sum will be 25 * 20 = 500

Now 500 + 300 = 800

and 15 + 20 = 35

So the mean is 500 / 35 = 100  / 7

Ans: the mean is 100 / 7 or 14 2 / 7 (mixed fraction) or 14.285714.....