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If average of four members is 20 and average of their squares is 500, then average of their products taken two at a time, is:
1. 366.7
2. 475
3. 550
4. 650

1 Answer

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Correct Answer - Option 1 : 366.7

Given 

Average of four number = 20

Formula used 

Average = Sum of observation/No. of observation 

(a + b + c + d)2 = a2 + b2 + c2 + d2 + 2(ab + bc + cd + da + bd + ac)

Calculation 

Let the number be p, q, r, s

Sum of observation = 20 × 4 = 80

⇒ p + q + r + s = 80

Sum of their squares = 500 × 4 = 2000

⇒ p2 + q2 + r2 + s2 = 2000 

⇒ 6400 = 2000 + 2(ab + bc + cd + da + bd + ac) 

⇒ ab + bc + ca + da + bd + ac = 2200 

Average of their products taken two at a time = 2200/6 = 366.7

∴ The required answer is 366.7

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