Statistics

If $\sum_{i=1}^9\left(x_i-5\right)=9$ and $\sum_{i=1}^9\left(x_i-5\right)^2=45$, then the standard deviation of the 9 items $x_1, x_2 \ldots, x_9$ is

If $\bar{x}_1$ and $\bar{x}_2$ are the means of two distributions such that $\bar{x}_1 \lt \bar{x}_2$ and $\bar{x}$ is the mean of the combined distribution, then

The mean deviation from the mean of the series $a, a+d, a+2 d, \ldots, a+2 n d$, is

If $\sum_{i=1}^{10}\left(x_i-3\right)=7$ and $\sum_{i=1}^{10}\left(x_i-3\right)^2=27$, then the standard deviation of the 10 items

The mean deviation from the mean for the set of observations $-1,0,4$ is

The variance of first $n$ natural numbers is

If the standard deviation of $0,1,2,...,9$ is $k$, then the standard deviation of $10,11,12,...,19$ is

The ratio of the variance of first $n$ positive integral multiples of $4$ to the variance of first $n$ positive odd numbers is

If the variance of the first $50$ odd natural numbers is $V_{1}$and the varianceof next $50$ odd natural numbers is $V_{2}$,then $V_{1}+V_{2}$ is equal to

The marks obtained by $9$ students in a chemistry test are$50,69,20,33,53,39,40,65$and $59$. If the mean deviation about the median of this data is$\lambda\,$, then the value of$\frac{9\lambda\,}{10}$is equal to

If the variance of the following data : $6,8,10,12,14,16,18,20,22,24$ is $K$, then the value of $\frac{K}{11}$ is

A number equal to $2$ times the mean and with a frequency equal to $k$ is inserted in a data having$n$ observations. If the new mean is $\frac{4}{3}$ times the old mean, then the value of$\frac{k}{n}$ is