The arithmetic mean of the following data is $14$ . Find the value of $k$ .
$x$ : $5$ $10$ $15$ $20$ $25$
$f$ : $7$ $k$ $8$ $4$ $5$

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Solution

Arithmetic Mean = $\frac{\sum x_{i} f_{i}}{\sum f_{i}}$

$\Rightarrow$ Arithmetic mean = $\frac{(5 \times 7) + (10 \times k) + (15 \times 8) + (20 \times 4) + (25 \times 5)}{7 + k + 8 + 4 + 5}$

$\Rightarrow$ arithmetic mean = $\frac{35 + 10 k + 120 + 80 + 125}{7 + k + 8 + 4 + 5} = 14$

$\Rightarrow 336 + 14 k = 360 + 10 k$

$\Rightarrow 4 k = 24$

$\Rightarrow k = 6$

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Similar questions

The arithmetic mean of the following data is 14. Find the value of k.
$x_{i}$ : 5 10 15 20 25
$f_{i}$ : 7 k 8 4 5.

x_i:	5	10	15	20	25
f_i:	7	k	8	4	5

25

k

$x_{i}$ :	$5$	$15$	$25$	$35$	$45$
$f_{i}$ :	$3$	$k$	$3$	$6$	$2$

x	$5$	$10$	$15$	$20$	$25$	$30$
f	$4$	$5$	$7$	$4$	$3$	$2$

x_i:	5	15	25	35	45
f_i:	3	k	3	6	2

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