If the mean of x in distribution
Variate x
1
2
3 4
5
Frequency of x
4
5
k
1
2
is 2.6, then the value of k is

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Solution

The correct option is A 8
$x_{i}$ $f_{i}$ $f_{i} x_{i}$
$1$ $4$ $4$
$2$ $5$ $10$
$3$ $k$ $3 k$
$4$ $1$ $4$
$5$ $2$ $10$
$\sum f_{i} = 12 + k$ $\sum f_{i} x_{i} = 28 + 3 k$
$\Rightarrow$ $¯ ¯ ¯ x = \frac{\sum f_{i} x_{i}}{\sum f_{i}}$

$\Rightarrow$ $2.6 = \frac{28 + 3 k}{12 + k}$

$\Rightarrow$ $31.2 + 2.6 k = 28 + 3 k$
$\Rightarrow$ $0.4 k = 3.2$
$∴$ $k = 8$

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Similar questions

Variate X	1	2	3	4	5
Frequency of X	4	5	k	1	2

\begin{matrix} Variable x & 1 & 2 & 3 & 4 & 5 Frequency of x & 4 & 5 & Y & 1 & 2 \end{matrix}

Variable (x):	1	2	3	4	5
Frequency	4	5	y	1	2

2.6

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

2.6

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

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