The arithmetic mean of the following data is $25$ , find the value of $k$ .
$x_{i}$ : $5$ $15$ $25$ $35$ $45$
$f_{i}$ : $3$ $k$ $3$ $6$ $2$

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Solution

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

$\Rightarrow$ arithmetic mean = $\frac{(5 \times 3) + (15 \times k) + (25 \times 3) + (35 \times 6) + (45 \times 2)}{3 + k + 3 + 6 + 2}$

$\Rightarrow$ arithmetic mean = $\frac{15 + 15 k + 75 + 210 + 90}{3 + k + 3 + 6 + 2} = 25$

$\Rightarrow 350 + 25 k = 390 + 15 k$

$\Rightarrow k = 4$

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Similar questions

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

14

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$x$ :	$5$	$10$	$15$	$20$	$25$
$f$ :	$7$	$k$	$8$	$4$	$5$

18.75

p

$x_{i}$ :	$10$	$15$	$p$	$25$	$30$
$f_{i}$ :	$5$	$10$	$7$	$8$	$2$

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.

$x_{i}$	$10$	$15$	$18$	$20$	$25$
$f_{i}$	$3$	$2$	$5$	$8$	$2$

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