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

Let the other two numbers be
$\alpha and\beta .$

$\overline{x}=4,N=5and\frac{\sum (x-\overline{x}{)}^2}{N}=5.2\Rightarrow \sum (x-\overline{x}{)}^2=(5.2)5\therefore \sum (x-\overline{x}{)}^2=26\therefore (1-4{)}^2+(2-4{)}^2+(6-4{)}^2+(\alpha -4{)}^2+(\beta -4{)}^2=26\therefore (\alpha -4{)}^2+(\beta -4{)}^2=9Also,\frac{1+2+6+\alpha +\beta }{5}=4\therefore \alpha +\beta =20-9=11Clearly4,7onlysatisfytheaboveequationin\alpha ,\beta .Hencerequirednumbersare4,7.$