Variance and Standard Deviation

For $2n$ observations $a_1,-a_1,a_2,-a_2,a_3,-a_3,\mathrm{.........},a_n,-a_n$ where all $a$'s are distinct. Let $\overline{x}$, $\sigma$ and $M$ denotes mean, standard deviation and median, respectively. Then which of the following option is incorrect when $n$ is an odd integer?

The variance of ${}^{n}C_1, 2 {}^{n}C_2, 3 {}^{n}C_3,....n\times {}^{n}C_n$ is

Let $x$ denotes the mean of data $3, x, 2$ and $4$, then choose the correct statement.

The following gives the number of books taken in a school library in $7$ days. Find the variance(up to two decimals) of the books taken.

$7,9,12,15,5,4,11$

Find the $S.D.$ for the number of days patients admitted in a hospital(up to two decimals).

If the coefficient of variation is $50\%$ and standard deviation is $4$, then find mean.

The expression of standard deviation as a percentage of the mean is the coefficient of variation.

The mean and standard deviation from $18$ observations are $14$ and $12$. If additional observation $8$ is to be included, find corrected mean and variance.

Find the standard deviation for the distribution given below:

A retailer uses two different formulas for predicting monthly sales. The first formula has an average of $700$ records, and a standard deviation of $35$ records. The second formula has an average of $300$ records, and a standard deviation of $16$ records. What is the ratio of coefficient of variation of first formula to that of second formula?(upto two decimals).

The standard deviation of a set of $50$ observations is $8$. What is new value of standard deviation if each observation is multiplied by $2$.

The square root of variance of a distribution is known as

Find the standard deviation of the following set of data:

$x, \frac{x}{7}, \frac{x}{3}, \frac{2}{7}x, \frac{x}{4}$ where $x = 840.$

What will be the standard deviation of the set of observations given below is mean of the following data is $7$.

Data: $5, 7, 6, 6, 9, x$.

Find the standard deviation of the following data.

Data: $18, 25, 27, 23$ and $17$.

If coefficient of variation is $25\%$ and mean is then find the value of standard deviation for the given data.

If standard deviation of a set of observations is $5$, by what percent is variance more or less than standard deviation?

Find the variance of the set $\left\{x\in \mathrm{\mathbb{N}}:0<x<2\right\}$.

Find the variance of the numbers $3.6, 6.4, 8.1, 5.0, 4.2, 7.3.$

Find the mean of the set $\left\{x:x^2-1=0\right\}$.