The mean and variance of 7 observations are 8 and 16, respectively. If five of the observations are 2, 4, 10, 12 and 14. Find the remaining two observations.

Let the
remaining two observations be *x* and* y*.

The
observations are 2, 4, 10, 12, 14, *x*, *y*.

From (1), we obtain

*x*^{2}
+ *y*^{2} + 2*xy* = 196 … (3)

From (2) and (3), we obtain

2*xy *=
196 – 100

⇒
2*xy* = 96 … (4)

Subtracting (4) from (2), we obtain

*x*^{2}
+ *y*^{2 }– 2*xy* = 100 – 96

⇒
(*x* – *y*)^{2} = 4

⇒ *x*
– *y* = ±
2 … (5)

Therefore, from (1) and (5), we obtain

*x* =
8 and *y* = 6 when *x* – *y* = 2

*x* =
6 and *y* = 8 when *x* – *y* = – 2

Thus, the remaining observations are 6 and 8.

**
**