Question

The mean of the following data is $50.$ Find the value of a and hence the frequencies of $30$ and $70.$
$\begin{array}{cccccc}X& 10& 30& 50& 70& 90\\ F& 17& 5a+3& 32& 7a-11& 19\end{array}$

• A. $28$ and $34$
• B. $68$ and $24$
• C. $28$ and $24$
• D. None of these

Answer 1

The correct option is C $28$ and $24$

X	$10$	$30$	$50$	$70$	$90$
F	$17$	$5\alpha +3$	$32$	$7\alpha -11$	$19$

Mean = $\frac{\sum fixi}{\sum fi}=50$

$50=\frac{10\times 17+30(5\alpha +3)+50\times 32+70(7\alpha -11)+90\times 19}{17+5\alpha +3+32+7\alpha -11+19}$

$50(12\alpha +60)=640\alpha +2800$

$3000+600\alpha =640\alpha +2800$

$40\alpha =200$

$\alpha =5$

frequency of $30=5\alpha +3=25+3=28$

frequency of $70=7\alpha -11=35-11=24$.