R S Aggarwal Solutions for Exercise 3: EXERCISE 1C

If the standard deviation of the numbers $2,3,2 x, 11$ is $3.5$, calculate the value of $x$ which is a natural number.

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

The variance of $20$ observations in $5$. If each observation is multiplied by $2$. Find the variance of the following observations.

The mean and variance of five observations are $6$ and $4$ respectively. If three of these are $5,7$ and $9$, find the other two observations.

The mean and variance of five observations are $4.4$ and $8.24$ respectively. If three of these are $1,2$ and $6$, find the other two observations.

The mean and standard deviation of $18$ observations are found to be $7$ and $4$ respectively. On rechecking it was found that an observation $12$ was misread as $21$. Calculate the correct standard deviation.

For a group of $200$ candidates, the mean and standard deviations of scores were found to be $40$ and $15$ respectively. Later on it was discovered that the score of $43$ was misread as $34$. Find the correct standard deviation. 

The mean and standard deviations of a group of $100$ observations were found to be $20$ and $3$ respectively. Later on it was found that three observations $21,12$ and $18$ were incorrect. Find the mean and standard deviation if the incorrect observations were omitted.