If the mean of following frequency distribution. is $2.6$ , then the value of f is:
$x_{i}$
1 2 3 4 5
$f_{i}$ 5 4 f 2 3

3

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1

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8

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None of these

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Solution

The correct option is B $1$
Frequency Distribution table:
$x i$ $f_{i}$ $f_{i} x_{i}$
$1$ $5$ $5$
$2$ $4$ $8$
$3$ $f$ $3 f$
$4$ $2$ $8$
$5$ $3$ $15$
$N = Σ f_{i} = 14 + f$
$Σ f_{i} x_{i} = 36 + 3 f$

Mean $= 2.6 = \frac{36 + 3 f}{14 + f}$
$∴ 36.4 + 2.6 f = 36 + 3 f$
$∴ 0.4 f = 0.4$
$∴ f = 1$
Hence, option $B$ is correct.

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Similar questions

2.6

$x_{i}$	$1$	$2$	$3$	$4$	$5$
$f_{i}$	$5$	$4$	$f$	$2$	$3$

5

b

$x_{i}$ :	3	5	7	4
$f_{i}$ :	2	$a$	5	$b$

15

p

Variable $(x_{i})$	$10$	$12$	$14$	$16$	$18$
Frequency $(f_{i})$	$13$	$p$	$15$	$32$	$28$

$x_{i}$	$10$	$12$	$15$	$25$
$f_{i}$	$2$	$3$	$7$	$8$

$x_{i}$	3	6	9	12
$f_{i}$	1	2	3	4

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