Question

plz help the question from mean and varriance

Answer 1

Please mark brainliest

Answer 2

Let x and y be the remaining two observations.
Thus,
The observations are 2, 4, 10, 12, 14, x and y.

Given,

Mean = 8

Or (2+4+10+12+14+x+y)/7 = 8

Or x + y + 42 = 56

Or x + y = 14...............(i)

Also,

Variance = 16

Or $\frac{1}{n}$∑(xᵢ - Mean) = 16

Or $\frac{1}{7}$∑ (xᵢ - 8) = 16

Or ∑ (xᵢ - 8) = 112

Or (2-8)²+(4-8)²+(10-8)²+(12-8)²+(14-8)²+(x-8)²+(y-8)² = 112

Or (-6)²+(-4)²+(2)²+(4)²+(6)²+x² -16x + 64 + y² - 16y + 64 = 112

Or 36 + 16+4+16+36+64+64+ x² + y² -16(x+y) = 112

Or 236 + x² + y² - 16(x+y) = 112

Or x² + y² - 16 × 14 = -124

Or x² + y² - 224 = -124

Or x² + y² = 100..........(ii)

Now,

(i)⇒ x+ y = 14

Or (x+y)² = 14

Or x² + y² + 2xy = 196

Or 100 + 2xy = 196 [From ii]

Or 2xy = 96

Or xy = 48

Or x = 48/y ...............(iii)

Now,

Substituting the value of x in (i), we get

48/y +y = 14

Or 48+y²/y = 14

Or 48 + y² = 14 y

Or y² -14y + 48 = 0

Or y² -(8+6)y + 48 = 0

Or y² -8y -6y + 48 = 0

Or y(y-8) -6(y-8) =0

Or (y-8)(y-6) = 0

Or y = 8 or 6

Now,

(iii)⇒ x = 48/y = 48/8 or 48/6

x = 6 or 8

Thus, 6 and 8 are the remaining observations.