Answer :

Let us assume the remaining two observations be x and y

The given observations in the question are 2, 4, 10, 12, 14, x, y

x + y = 14 (i)

It is also given in the question that,

Variance = 16

We know that,

x^{2} + y^{2} = 112 - 12

x^{2} + y^{2} = 100 (ii)

Thus, by using (i) we have:

x^{2} + y^{2} + 2xy = 196 (iii)

Now, from equation (ii) and (iii) we have:

2xy = 196 – 100

2xy = 96 (iv)

Now subtracting equation (iv) from (ii), we get:

x^{2} + y^{2} – 2xy = 100 – 96

(x – y)^{2} = 4

x – y = 2 (v)

Hence, from equation (i) and (v) we have:

When x – y = 2 then x = 8 and y = 6

And, when x – y = - 2 then x = 6 and y = 8

∴ The remaining observations are 6 and 8

Rate this question :

The sum and the sRS Aggarwal - Mathematics

If x_{1},RD Sharma - Mathematics

The mean and variRS Aggarwal - Mathematics

If the sum of theRD Sharma - Mathematics

The mean and stanRS Aggarwal - Mathematics

Following are theRD Sharma - Mathematics

The mean and variRS Aggarwal - Mathematics

The following resRS Aggarwal - Mathematics

Coefficient of vaRS Aggarwal - Mathematics

The following resRS Aggarwal - Mathematics