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

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 and variance for the following frequency distribution:

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

Find the mean, variance and standard deviation using short-cut method Height in cms:

The diameters of circles (in mm) drawn in a design are given below:

Calculate the standard deviation and mean diameter of the circles. [ Hint First make the data continuous by making the classes as 32.5-36.5, 36.5-40.5, 40.5-44.5, 44.5 - 48.5, 48.5 - 52.5 and then proceed.]

Find the mean and variance for the following frequency distribution:

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

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.

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

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

Find the mean deviation about median for the following data:

 

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 mean for the data:

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: (i) If wrong item is omitted.

Find the mean deviation about the mean for the data:

 

Find the mean deviation about the median for the data:
$x_i$: 5 7 9 10 12 15
$f_i$: 8 6 2 2 2 6

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

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