Question
Download Solution PDFIf the average of s numbers is r4 and the average of r numbers is s4, the find the average of all r + s numbers?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The average of s numbers is r4 and the average of r numbers is s4.
Concept used:
1. a3 + b3 = (a + b)(a2 - ab + b2)
2. Total = Average × Number of entities
Calculation:
Total sum of s numbers = s × r4 = sr4
Total sum of r numbers = r × s4 = rs4
Now, the average of all r + s numbers
⇒ (rs4 + sr4) ÷ (r + s)
⇒ rs(s3 + r3) ÷ (r + s)
⇒ rs(s + r)(s2 - sr + r2) ÷ (r + s)
⇒ rs(s2 - sr + r2)
⇒ rs \((r^2 + s^2 - rs) \)
∴ The average of all r + s numbers is rs \((r^2 + s^2 - rs) \).
Last updated on Jun 13, 2025
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