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 data:

Find the mean and variance for the following frequency distribution:

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

Find the mean and variance for the following frequency distribution:

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

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

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

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.

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

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

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.

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:

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 median for the following data: