If the variance of the frequency distribution is $160$,then the value of $c \in N$ is

$X$	$c$	$2c$	$3c$	$4c$	$5c$	$6c$
$f$	$2$	$1$	$1$	$1$	$1$	$1$

An analysis of monthly wages paid to workers in two firms $A$ and $B$,belonging to the same industry,gives the following results:

\text{Particulars}	\text{Firm } $A$ \text{ and Firm } $B$
\text{No. of wage earners}	$A: 586, B: 648$
\text{Mean of monthly wages}	$A: Rs. 5253, B: Rs. 5253$
\text{Variance of wages}	$A: 100, B: 121$

Which firm,$A$ or $B,$ shows greater variability in individual wages?

The mean and variance of six observations are $6$ and $12$ respectively. If each observation is multiplied by $3$,then the new variance of the resulting observations is:

All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of $10$ to each of the students. Which of the following statistical measures will not change even after the grace marks were given?

The coefficient of variation and standard deviation of an ungrouped data are $60$ and $21$ respectively. If $15$ is added to every observation of the data,then the coefficient of variation of the new data is

For a statistical data $x_1, x_2, \ldots, x_{10}$ of $10$ values,a student obtained the mean as $5.5$ and $\sum_{i=1}^{10} x_i^2 = 371$. He later found that he had noted two values in the data incorrectly as $4$ and $5$,instead of the correct values $6$ and $8$,respectively. The variance of the corrected data is