Find the mean and variance for the following frequency distribution:

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

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

Find the mean deviation about the mean for the data:

 

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

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

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

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

Find the mean and variance for the following frequency distribution:

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: 13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17

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

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

Calculate the mean deviation about median age for the age distribution of 100 persons given below:

[Hint Convert the given data into continuous frequency distribution by subtracting 0.5 from the lower limit and adding 0.5 to the upper limit of each class interval]

Find the mean deviation about median for the following 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: (ii) If it is replaced by 12.