Standard Deviation about Median

Q. Find the standard deviation for the following data:
$\begin{array}{cccccc}{x}_i& 3& 8& 13& 18& 23\\ f_i& 7& 10& 15& 10& 6\end{array}$

1. 5.37
2. 15.92
3. 6.12
4. 13.87

Q. The standard deviation $\sigma$ of $(q+p{)}^{16}$ is $2.$ The mean of distribution is

Q. Find the standard deviation for the following data:
$\begin{array}{cccccc}{x}_i& 3& 8& 13& 18& 23\\ f_i& 7& 10& 15& 10& 6\end{array}$

1. 5.37
2. 15.92
3. 6.12
4. 13.87

Q. If the standard deviation of number $3,4,8,14,16$ is $5.21,$ then the standard deviation of number $6,7,11,17,19$ is

1. $1.74$
2. $5.21$
3. $15.63$
4. $10.42$

Q. The sum of the squares of deviation of 10 observations from their mean 50 is 250, then coefficient of variation is

1. 10%
2. 50%
3. 40%
4. none of these

Q. If the mean and variance of eight numbers $3,$ $7,$ $9,$ $12,$ $13,$ $20,$ $x,$ $y$ are $10$ and $25$ respectively, then which of the following is false $(x>y)$

1. $x^2+y^2=148$
2. $xy=54$
3. $x-y=2\sqrt{10}$
4. $x,y$ are rational numbers

Q. The sum of the squares of deviations of 10 items about mean 50 is 250 .The coefficient of variation is

1. 10%
2. 50%
3. none of these
4. 30%

Q. Standard deviation for n observations $x_1,x_2,\dots x_n$ is 5, then the standard deviation for n observations $x_1+1,x_2+1,\dots x_{n+1}$ will be ___

Q. Standard deviation for n observations $x_1,x_2,\dots x_n$ is 5, then the standard deviation for n observations $x_1+1,x_2+1,\dots x_{n+1}$ will be ___

Q. Standard deviation for n observations $x_1,x_2\dots x_n$ is '5' then the standard deviation of n observations $5x_1,5x_2,\dots 5x_n$ will be ___

Q. The variance of numbers $x_1,x_2,x_3,.....x_n$ is V. Consider the following statements :
1. If every $x_1$, is increased by 2, the variance of the new set of numbers is V.
2. If the numbers $x_1$ is squared, the variance of the new set is $V^2$.
Which of the following statements is/are correct ?

1. 1 only
2. 2 only
3. Neither 1 nor 2
4. Both 1 and 2

Q. Standard deviation for n observations $x_1,x_2\dots x_n$ is '5' then the standard deviation of n observations $5x_1,5x_2,\dots 5x_n$ will be ___

Q. Find the standard deviation for the following data:
$\begin{array}{cccccc}{x}_i& 3& 8& 13& 18& 23\\ f_i& 7& 10& 15& 10& 6\end{array}$

1. 5.37
2. 6.12
3. 15.92
4. 13.87

Q. Find $a$, $b$, $c$ so that the coefficient of $x^n$ in the expansion of $\frac{a+bx+c{x}^2}{{(1-x)}^3}$ may be $n^2+1$.

Q. The degree to which numerical data tend to spread about value is called

1. variation
2. mode
3. median
4. mean