Variance and Standard Deviation

Calculate the standard deviation of the following data :

Find the change of origin for the observations $x$ and $z$. Also find the change of scale for the observations $x$ and $y$.

$x: 1,2,3,4$

$y:4,8,12,16$

$z:4,5,6,7$ 

Find the change of origin for the observations $x$ and $z$. Also find the change of scale for the observations $x$ and $y$.

$x: 2,3,4,5$

$y:8,12,16,20$

$z:5,6,7,8$ 

Find the change of origin for the observations $x$ and $z$. Also find the change of scale for the observations $x$ and $y$.

$x: 1,2,3,4,5$

$y:4,8,12,16,20$

$z:4,5,6,7,8$ 

Find the change of origin for the observations $x$ and $z$. Also find the change of scale for the observations $x$ and $y$.

$x: 1,2,3,4,5$

$y:3,6,9,12,15$

$z:3,4,5,6,7$ 

Find the change of origin for the observations $x$ and $z$. Also find the change of scale for the observations $x$ and $y$.

$x: 1,2,3,4,5$

$y:2,4,6,8,10$

$z:2,3,4,5,6$ 

For a group of $50$ male workers the mean and standard deviation of their daily wages are $63$ dollars and $9$ dollars respectively. For a group of $40$ female workers these values are $54$ dollars and $6$ dollars respectively. Find the mean and standard deviation of the combined group of $90$ workers.

The mean height of $200$ students is $65$ inches. The mean heights of boys and girls are $70$ inches and $62$ inches respectively and the standard deviations are $8$ and $10$ respectively. Find the number of boys and the combined S.D.

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

The mean and the standard deviation of data for $8$ items are $25$ and $5$ respectively. If two items $15$ and $25$ are added to this data, then the variance of new data is

The mean of $5$ observations is $15$ and variance is $9.$ If two observations having values $-5$ and $13$ are combined with these observations, then what will be the new variance?

If the variance of the data $12,14,18,19,21,36$ is $\lambda$, then the value of $3\lambda$ is equal to

If the mean and the variance of the numbers $a, b, \mathrm{8,} 5$ and $10$ are $6$ and $6.8$ respectively, then the value of $a^3+b^3$ is equal to

The variance of the first $20$ positive integral multiples of $4$ is equal to

Find the standard deviation (correct upto two decimals) for the numbers $4, 6, 10, 12, 7, 8, 13, 12$.

Let $x_1, x_2,...., x_n$ be $n$ observations such that $\sum {\left(x_i\right)}^2=400$ and $\sum x_i=40$, then a possible value of $n$ among the following is

The mean of two samples of sizes $40$ and $50$ were found to be $54$ and $63$ respectively. Their standard deviations were $6$ and $9$ respectively. The variance of the combined sample of size $90$ is

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

Find the range of the following data set:

$116, 124, 164, 150, 149, 114, 195, 128, 138, 203, 144$

Two sets each of $20$ observations, have the same standard derivation $5$. The first set has a mean $17$ and the second  mean $22$. Determine the standard deviation of the $x$ sets obtained by combining the given two sets.