If the mean and the standard deviation of the data $3, 5, 7, a, b$ are $5$ and $2$ respectively,then $a$ and $b$ are the roots of the equation:

If $x_1, x_2, \ldots, x_n$ are $n$ observations and $\bar{x}$ is their mean. If $\sum_{i=1}^{n}(x_i - \bar{x})^2$ is almost zero,then which of the following statements is true?

While calculating the mean and variance of $10$ readings,a student wrongly used the reading $52$ for the correct reading $25$. He obtained the mean and variance as $45$ and $16$ respectively. Find the correct mean and the variance.

If the algebraic sum of deviations of $20$ observations from $30$ is $20$,then the mean of the observations is:

In a set of $2n$ distinct observations,each of the observations below the median is increased by $5$ and each of the remaining observations is decreased by $3$. Then the mean of the new set of observations

The mean life of a sample of $60$ bulbs was $650$ hours and the standard deviation was $8$ hours. $A$ second sample of $80$ bulbs has a mean life of $660$ hours and standard deviation $7$ hours. Find the overall standard deviation.