Find the mean deviation about the mean of the distribution.

Find the mean deviation about the median of the following distribution.

3 Calculate the mean deviation about the mean of the set of first $n$ natural numbers when $n$ is an odd number.

Calculate the mean deviation about the mean of the set of first $n$ natural numbers when $n$ is an even number.

Find the standard deviation of first n natural numbers.

The mean and standard deviation of some data for the time taken to complete a test are calculated with the following results Number of observation $=25$, mean $=18.2 \mathrm{~s}$, standard, deviation $=3.25 \mathrm{~s}$ Further, another set of 15 observations $x_1 x_2 \ldots x_{15}$, also in seconds, is now available and we have $\sum_\limits{i=1}^{15} x_i=279$ and $\sum_\limits{i=1}^{15} x_i^2=5524$. Calculate the standard derivation based on all 40 observations.

The mean and standard deviation of a set of $n_1$ observations are $\bar{x}_1$ and $s_1$, respectively while the mean and standard deviation of another set of $n_2$ observations are $\bar{x}_2$ and $s_2$, respectively. Show that the standard deviation of the combined set of $\left(n_1+n_2\right)$ observations is given by

$$S D=\sqrt{\frac{n_1\left(s_1\right)^2+n_2\left(s_2\right)^2}{n_1+n_2}+\frac{n_1 n_2\left(\bar{x}_1-\bar{x}_2\right)^2}{\left(n_1-n_2\right)^2}}$$

Two sets each of 20 observations, have the same standard deviation 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.

The frequency distribution

where, A is a positive integer, has a variance of 160. Determine the value of A.

For the frequency distribution

Find the standard distribution.

There are 60 students in a class. The following is the frequency distribution of the marks obtained by the students in a test.

where, x is positive integer. Determine the mean and standard deviation of the marks.

The mean life of a sample of 60 bulbs was 650 h and the standard deviation was 8 h . If a second sample of 80 bulbs has a mean life of 660 h and standard deviation 7 h , then find the over all standard deviation.

If mean and standard deviation of 100 items are 50 and 4 respectively, then find the sum of all the item and the sum of the squares of item.

If for distribution $\Sigma(x-5)=3, \Sigma(x-5)^2=43$ and total number of item is 18 . Find the mean and standard deviation.

Find the mean and variance of the frequency distribution given below.

Calculate the mean deviation about the mean for the following frequency distribution.

Calculate the mean deviation from the median of the following data.

Determine the mean and standard deviation for the following distribution.

The weights of coffee in 70 jars is shown in the following table

Determine variance and standard deviation of the above distribution.

Determine mean and standard deviation of first n terms of an AP whose first term is a and common difference is d.

Following are the marks obtained, out of 100, by two students Ravi and Hashina in 10 tests.

Who is more intelligent and who is more consistent?

Mean and standard deviation of 100 observations were found to be 40 and 10 , respectively. If at the time of calculation two observations were wrongly taken as 30 and 70 in place of 3 and 27 respectively, then find the correct standard deviation.

3 While calculating the mean and variance of 10 readings, a student wrongly used the reading 52 for the correct reading 25 . He obtained the mean and variance as 45 and 16, respectively. Find the correct mean and the variance.

The mean deviation of the data $3,10,10,4,7,10,5$ from the mean is

Mean deviation for $n$ observations $x_1, x_2, \ldots, x_n$ from their mean $\bar{x}$ is given by

When tested, the lives (in hours) of 5 bulbs were noted as follows

$$\text { 1357, 1090, 1666, 1494, } 1623$$

The mean deviations (in hours) from their mean is

Following are the marks obtained by 9 students in a mathematics test

$$50,69,20,33,53,39,40,65,59$$

The mean deviation from the median is

The standard deviation of data $6,5,9,13,12,8$ and 10 is

If $x_1, x_2, \ldots, x_n$ be $n$ observations and $\bar{x}$ be their arithmetic mean. Then, formula for the standard deviation is given by

If the mean of 100 observations is 50 and their standard deviation is 5 , than the sum of all squares of all the observations is

If $a, b, c, d$ and $e$ be the observations with mean $m$ and standard deviation $s$, then find the standard deviation of the observations $a+k$, $b+k, c+k, d+k$ and $e+k$ is

If $x_1, x_2, x_3, x_4$ and $x_5$ be the observations with mean $m$ and standard deviation $s$ then, the standard deviation of the observations $k x_1, k x_2$, $k x_3, k x_4$ and $k x_5$ is

Let $x_1, x_2, \ldots x_n$ be $n$ observations. Let $w_i=l x_i+k$ for $i=1,2, \ldots, n$, where $l$ and $k$ are constants. If the mean of $x_i$ 's is 48 and their standard deviation is 12 , the mean of $w_i{ }^{\prime} s$ is 55 and standard deviation of $w_i{ }^{\prime} s$ is 15 , then the value of $l$ and $k$ should be

The standard deviations for first natural numbers is

Consider the numbers $1,2,3,4,5,6,7,8,9$, and 10 . If 1 is added to each number the variance of the numbers, so obtained is

Consider the first 10 positive integers. If we multiply each number by $-$1 and, then add 1 to each number, the variance of the numbers, so obtained is

The following information relates to a sample of size 60, $\Sigma x^2=18000$, and $\Sigma x=960$. Then, the variance is

If the coefficient of variation of two distributions are 50, 60 and their arithmetic means are 30 and 25 respectively, then the difference of their standard deviation is

The standard deviation of some temperature data in ${ }^{\circ} \mathrm{C}$ is 5 . If the data were converted into ${ }^{\circ} \mathrm{F}$, then the variance would be

Coefficient of variation $=\frac{\cdots}{\text { Mean }} \times 100$

If $\overline{\boldsymbol{x}}$ is the mean of $n$ values of $\boldsymbol{x}$, then $\sum_\limits{i=1}^n\left(\boldsymbol{x}_1-\overline{\boldsymbol{x}}\right)$ is always equal to .......... . If $a$ has any value other than $\overline{\boldsymbol{x}}$, then $\sum_\limits{i=1}^n\left(\boldsymbol{x}_i-\overline{\boldsymbol{x}}\right)^2$ is ................. than $\sum\left(x_i-a\right)^2$

If the variance of a data is 121 , then the standard deviation of the data is ............ .

The standard deviation of a data is ........... of any change in origin but is ............. of change of scale.

The sum of squares of the deviations of the values of the variable is ........... when taken about their arithmetic mean.

The mean deviation of the data is ........... when measured from the median.

The standard deviation is ........... to the mean deviation taken from the arithmetic mean.