If the mean of two samples of sizes $20$ and $30$ are $25$ and $10$ respectively,and their variances are $9$ and $16$ respectively,then their combined variance is:

The mean and variance of seven observations are $8$ and $16$,respectively. If $5$ of the observations are $2, 4, 10, 12, 14$,then the product of the remaining two observations is

For a group of $100$ students,the mean $\bar{x}_1$ and the standard deviation $\sigma_1$ of their marks were found to be $40$ and $15$ respectively. Later,it was observed that the scores $40$ and $50$ were misread as $30$ and $60$ respectively. If the mean and the standard deviation with the corrected observations of the scores are $\bar{x}_2$ and $\sigma_2$ respectively,then:

The mean of $10$ terms is $3$. If the first term is increased by $1$,the second by $2$,and so on,then the new mean is:

In a city,the total income of all people with a salary below $₹ 10,000$ per annum is less than the total income of all people with a salary above $₹ 10,000$ per annum. If the salaries of people in the first group increase by $5 \%$ and the salaries of people in the second group decrease by $5 \%$,then the average income of all people:

The mean of $5$ numbers is $18$. If one number is excluded,their mean becomes $16$. Then the excluded number is