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

Mean = $fraction numerator begin display style stack sum f subscript i x subscript i with i equals 1 below end style over denominator N end fraction$ = $fraction numerator 5 cross times 3 plus 15 k plus 25 cross times 3 plus 35 cross times 6 plus 45 cross times 2 over denominator 3 plus k plus 3 plus 6 plus 2 end fraction equals fraction numerator 15 plus 15 k plus 75 plus 210 plus 90 over denominator 14 plus k end fraction$

25= $fraction numerator 15 k plus 390 over denominator 14 plus k end fraction$

350 + 25k = 15k + 390

10k = 40

k = 4

Hence k = 4

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Similar questions

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

17

P

Term(x)	10	15	20	25
Frequency(f)	7	10	P	6

14

k

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

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

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