The average of v numbers is w
2
and that of w numbers is v
2
. Then the average of all the numbers is:
- Avw
2 - Bv+w
- Cvw
- Dv
2
+w
2
Solution & Step-by-step Explanation
Sum of the first group of v numbers:
Sum
1
=v×w
2
=vw
2
Sum of the second group of w numbers:
Sum
2
=w×v
2
=wv
2
Total count of all numbers = v+w
Total sum of all numbers = vw
2
+wv
2
=vw(w+v)
Now, calculate the overall average:
Average=
Total Count
Total Sum
Average=
v+w
vw(v+w)
=vw
Sum
1
=v×w
2
=vw
2
Sum of the second group of w numbers:
Sum
2
=w×v
2
=wv
2
Total count of all numbers = v+w
Total sum of all numbers = vw
2
+wv
2
=vw(w+v)
Now, calculate the overall average:
Average=
Total Count
Total Sum
Average=
v+w
vw(v+w)
=vw