The average of 8 numbers is 19. The average of first and sixth numbers is 17 and that of the third, fifth and seventh numbers is \(24\frac{…

We know that, Average = Sum of all observations/Number of observations

According to the given information,

Average of 8 numbers is 19

? The average of first and sixth numbers is 17

first number + sixth number = 17 × 2 = 34

And, since Average of the third, fifth and seventh numbers is $(24\frac{1}{3})$

∴ third number + fifth number + seventh number $(= \;24\frac{1}{3}\; \times 3\; = \;73)$

Now, since the second number is less than the fourth number by 8, and greater than the eighth number by 2, let the second number be x thus, fourth number would be x + 8, and eighth number would be x - 2.

Thus,

19 = (sum of all eight numbers)/8

$(\Rightarrow \frac{{x\; + \;x\; + \;8\; + \;x\; - \;2\; + \;73\; + \;34\;}}{8} = 19)$

⇒ 3x + 113 = 152

⇒ 3x = 39

⇒ x = 13

Hence fourth number = 13 + 8 = 21

eighth number = 13 - 2 = 11

Required sum = 21 + 11 = 32