Question

The mean of the following distribution is 50



X 10 30 50 70 90


F 17 5a+3 32 7a-11 19



Find the value of a.

Answer 1

$\huge\bold{ANSWER~:}$

$\large\bold{mean = \frac{sum~of~observations}{number~of~observations}}$

$\\ \\ 50 = \frac{17 - 5a + 3 + 32 + 7a - 11 + 19}{5} \\ \\ 50 = \frac{60 + 2a}{5} \\ \\ 50 \times 5 = 60 + 2a \\ \\ 250 - 60 = 2a \\ \\ a = 95$