Question

The mean of 10 numbers is 45..If one more is added to it the mean increases by 2..Therefore the number is_____​

Answer 1

Step-by-step explanation:

$Mean = \frac{Sum \: \: of \: \: Terms}{Number \: \: of \: \: Terms} \\ 45 = \frac{Sum \: \: of \: \: Terms}{10} \\ 45 \times 10 = Sum \: \: of \: \: Terms \\ \underline{ \underline{ \large \bf 450}} = Sum \: \: of \: \: Terms \\ \\ If \: \: one \: \: more \: \: is \: \: added \: \: to \: \: it \\ the \: \: mean \: \: increases \: \: by \: \: 2 \\ \\ Mean = \frac{Sum \: \: of \: \: Terms}{Number \: \: of \: \: Terms} \\ 47 = \frac{Sum \: \: of \: \: Terms}{11} \\ 47 \times 11 = Sum \: \: of \: \: Terms \\ \underline{ \underline{ \large \bf 517 }}= Sum \: \: of \: \: Terms \\ \\ Therefore, \: \: the \: \: number \: \: is: \\ Sum \: \: of \: \: 11 \: \: Terms - Sum \: \: of \: \: 10 \: \: Terms\\ = 517 - 450 \\ = \underline{ \underline{ \large \bf 67}}$