Question

The means of five observations is 4 and their variance is 5.2. If three of these observations are 1, 2, and 6, then the other two are:

• A. 2 and 9
• B. 3 and 8
• C. 4 and 7
• D. 5 and 6

Answer 1

The correct option is C 4 and 7

$\overline{X}=4,N=5and\frac{\sum (X-{\overline{X}}^2)}{N}=5.2\Rightarrow \sum (X-\overline{X}{)}^2=(5.2)\times 5\therefore \sum (X-\overline{X}{)}^2=26$
Let a and b be the other two numbers.
$\therefore (1-4{)}^2+(2-4{)}^2+(6-4{)}^2+(a-4{)}^2+(b-4{)}^2=26\therefore (a-4{)}^2+(b-4{)}^2=9Also,\frac{1+2+6+\alpha +\beta }{5}=4\therefore \alpha +\beta =20-9=11$

The numbers 4 and 7 satisfy both these conditions.