R D Sharma Solutions for Chapter: Statistics, Exercise 4: EXERCISE 32.4

Find the mean, variance and standard deviation for the following data:

$6, 7, 10, 12, 13, 4, 8, 12$.

Find the mean, variance and standard deviation for the following data:

$227, 235, 255, 269, 292, 299, 312, 321, 333, 348$.

Find the mean, variance and standard deviation for the following data:

$15, 22, 27, 11, 9, 21, 14, 9$..

The variance of $20$ observations is $5$. If each observation is multiplied by $2$ find the variance of the resulting observations.

The variance of $15$ observations is $6$. If each observation is increased by $8$ find the variance of the resulting observations.

The mean and standard deviation of $20$ observations are found to be $10$ and $2$ respectively. On rechecking it was found that an observation $8$ was incorrect. Calculate the correct mean and standard deviation in each of the following cases: If wrong item is omitted

The mean and standard deviation of $20$ observations are found to be $10$ and $2$ respectively. On rechecking it was found that an observation $8$ was incorrect. Calculate the correct mean and standard deviation in each of the following cases: if it is replaced by $12$.

The mean and standard deviation of a group of $100$ observations were found to be $20$ and $3$ respectively. Later on it was found that three observations were incorrect, which were recorded as $21, 21$ and $18$. Find the mean and standard deviation if the incorrect observations were omitted.