Question

the mean of five numbers is 7 After adding one more number the mean still remains 7 what is the new number

Answer 1

Mean =X = 27

No of observations = 7

 Sum of observations =  = 27 x 7 = 189

Let the included number be x

New Mean X' = 28

New number of observations = 8

New sum of observations =   28 x 8

                                              = 224 which is equal to  189+x

                                                     Thus x= 224-189 = 35   

Answer 2

Let the numbers be a,b,c,d,e
$\frac{a + b + c + d + e}{5} = 7 \\ \: \: a + b + c + d + e = 35$
let new number is x

$\frac{a + b + c + d + e + x}{6} = 7 \\ \: a + b + c + d + e + x = 42 \\ 35 + x = 42 \\ x = 7$
new number is 7