Embibe Experts Solutions for Chapter: Statistics, Exercise 2: Level 2

In a group of students, the mean weight of boys is $65 \mathrm{kg}$, and mean weight of girls is $55 \mathrm{kg}$. If the mean weight of all students of group is $61 \mathrm{kg}$, then the ratio of the number of boys and girls in the group is

If the mean of $n$ observations $1^2,2^2,3^2,......n^2$ is $\frac{46n}{11}$, then $n$ is equal to

For the set $A=\left\{x_1, x_2, x_3, x_4, x_5\right\}$ the variance is $4$ and the mean is $2.$ For the set $B=\left\{y_1, y_2, y_3, y_4, y_5\right\}$the variance is $5$ and the mean is $4.$ Then the variance of $A\cup B$ is

In any discrete series (when all the value are not same) the relationship between $\mathrm{M}.\mathrm{D}.$ about mean and $\mathrm{S}.\mathrm{D}.$ is-

If each observation of a distribution, whose variance is ${\sigma }^2$, is multiplied by $\lambda$, then the $\mathrm{S}.\mathrm{D}.$ of the new observations is:

If each observation of a distribution whose $\mathrm{S}.\mathrm{D}.$ is $\sigma$, is increased by $\lambda$, then the variance of the new observations is:

If the mean and standard deviation of the marks of $200$ candidates of IIT entrance test were found to be $40$ and $15$, respectively. Later, it was discovered that a score of $40$ was wrongly read as $50$. Then, the correct mean and standard deviation are

If the mean and the standard deviation of $10$ observations $x_1,x_2,\dots ,x_{10}$ are $2$ and $3$, respectively, then the mean of ${\left(x_1+1\right)}^2, {\left(x_2+1\right)}^2,\dots$ ${\left(x_{10}+1\right)}^2$ is equal to