The mean of the following distribution is 50
$x_{i}$ 10 30 50 70 90
$f_{i}$ 17 5a+3 32 7a-11 19
Find the value 'a'

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Solution

Mean $= \frac{\sum x_{i} f_{i}}{\sum x_{i}}$
$\Rightarrow \frac{10 (17) + 30 (5 a + 3) + 50 (32) + 70 (7 a - 11) + 90 (19)}{10 + 30 + 50 + 70 + 90} = 50$
$\Rightarrow \frac{2800 + 640 a}{250} = 50$
$\Rightarrow 2800 + 640 a = 12500$
$640 a = 9700$
$a = 15.15625$ .

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The mean of the following distribution is 50 xi 1030507090fi175a+3327a-1119Find the value 'a'

Mean =∑xifi∑xi⇒10(17)+30(5a+3)+50(32)+70(7a−11)+90(19)10+30+50+70+90=50⇒2800+640a250=50⇒2800+640a=12500640a=9700a=15.15625.

The mean of the following distribution is 50
$x_{i}$ 10 30 50 70 90
$f_{i}$ 17 5a+3 32 7a-11 19
Find the value 'a'

Mean $= \frac{\sum x_{i} f_{i}}{\sum x_{i}}$
$\Rightarrow \frac{10 (17) + 30 (5 a + 3) + 50 (32) + 70 (7 a - 11) + 90 (19)}{10 + 30 + 50 + 70 + 90} = 50$
$\Rightarrow \frac{2800 + 640 a}{250} = 50$
$\Rightarrow 2800 + 640 a = 12500$
$640 a = 9700$
$a = 15.15625$ .