Find the mean deviation about median for the following data:

 

Find the mean deviation about the mean for the data: 4, 7, 8, 9, 10, 12, 13, 17

The mean and standard deviation of six observations are 8 and 4, respectively. If each observation is multiplied by 3, find the new mean and new standard deviation of the resulting observations.

Find the mean deviation about the median for the data: 36, 72, 46, 42, 60, 45, 53, 46, 51, 49

Find the mean deviation about the mean for the data: 38, 70, 48, 40, 42, 55, 63, 46, 54, 44

The mean and variance of 7 observations are 8 and 16, respectively. If five of the observations are 2, 4, 10, 12, 14. Find the remaining two observations.

The mean and standard deviation of a group of 100 observations were found to be 20 and 3, respectively. Later on it was found that three observations were incorrect, which were recorded as 21, 21 and 18. Find the mean and standard deviation if the incorrect observations are omitted.

Find the mean deviation about the mean for the data:
$x_i$: 5 10 15 20 25
$f_i$: 7 4 6 3 5

Find the mean deviation about the median for the data: 13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17

Find the mean deviation about the mean for the data:
$x_i$: 10 30 50 70 90
$f_i$: 4 24 28 16 8

Given that $\overline{x}$ is the mean and $\sigma^2$ is the variance of $n$ observations $x_1, x_2, ..., x_n$. Prove that the mean and variance of the observations $ax_1, ax_2, ax_3, ...., ax_n$ are $a\overline{x}$ and $a^2\sigma^2$, respectively, ($a
eq 0$).

Find the mean deviation about the median for the data:
$x_i$: 15 21 27 30 35
$f_i$: 3 5 6 7 8

Find the mean and variance for: First $n$ natural numbers

The mean and standard deviation of 20 observations are found to be 10 and 2, respectively. On rechecking, it was found that an observation 8 was incorrect. Calculate the correct mean and standard deviation in each of the following cases: (ii) If it is replaced by 12.

Find the mean deviation about the mean for the data:

 

Find the mean and variance for the data: 6, 7, 10, 12, 13, 4, 8, 12

Find the mean and variance for: First 10 multiples of 3

Find the mean deviation about the mean for the data:

Find the mean and standard deviation using short-cut method.

The mean and variance of eight observations are 9 and 9.25, respectively. If six of the observations are 6, 7, 10, 12, 12 and 13, find the remaining two observations.