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} = a^{2} + b^{2} + c^{2} + d^{2} + 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

⇒ p^{2} + q^{2} + r^{2} + s^{2} = 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**