Question

If the average of the following data is $200.5$, find the value of $k$

• A. $-34.12$
• B. $34.10$
• C. $-38.12$
• D. $-30.15$

Answer 1

The correct option is A $-34.12$

Answer:- Given:- $\overline{x}=200.5$

Using frequency distribution table

x	f	xf
6	7	42
12	8	96
18	9	162
24	k	24k
30	5	150
36	4	144
	$\Sigma f_i=33+k$	$\Sigma x_i{f}_i=594+24k$

Average = $\frac{\Sigma fx}{\Sigma f}$

$\Rightarrow \overline{x}=\frac{594+24k}{33+k}$

$\Rightarrow 200.5=\frac{594+24k}{33+k}$

$\Rightarrow 200.5(33+k)=594+24k$

$\Rightarrow 6616.5+200.5k=594+24k$

$\Rightarrow 200.5k-24k=594-6616.5$

$\Rightarrow 176.5k=-6022.5$

$\Rightarrow k=-\frac{6022.5}{176.5}$

$\Rightarrow k=-34.12$