Arithmetic mean of nine observations is calculated as $38$. But in doing so, an observation $27$ is mistaken for $72$. Find the actual mean of the data.

Five years ago mean age of a family was $25$ years. If the present mean age of the family is $k$ years, find the value of $k$.

Two years ago the mean age of $40$ people was $11$ years. Now a person left the group and the mean age is changed to $12$ years. If the age of the person who left the group is $x$ years, find the value of $x$.

Find the sum of deviations of all observations of the data $5,8,10,15,22$ from their mean.

If sum of the $20$ deviations from the mean is $100$, then find the mean deviation.

Marks of $12$ students in a unit test are given as $4, 21, 13, 17, 5, 9, 10, 20, 19, 12, 20, 14$. Assume a mean and calculate the arithmetic mean of the data. Assume another number as mean and calculate the arithmetic mean again. Do you get the same result? Comment.

Arithmetic mean of marks (out of $25$) scored by $10$ students was $15$. One of the student, named Karishma enquired the other $9$ students and find the deviations from her marks are noted as $- 8, - 6, - 3, - 1, 0, 2, 3, 4, 6$. Find Karishma’s marks.

The sum of deviations of '$n$' observations from $25$ is $25$ and sum of deviations of the same '$n$' observations from $35$ is $-25$. Find the mean of the observations.

Find the median of the data: $3.3, 3.5, 3.1, 3.7, 3.2, 3.8$