Measures of Central Tendency

The arithmetic mean of $100$ observations is$24, 6$is added to each of the observations and then each of them is multiplied by $2.5$. Find the new arithmetic mean_____.

From the below given distribution find out mean.

$\begin{array}{cccccc}x:& 18& 29& 10& 11& 12\\ f:& 7& 2& 15& 10& 5\end{array}$

From the below given distribution find out mean.

$\begin{array}{cccccc}x:& 52& 20& 25& 30& 35\\ f:& 7& 15& 9& 17& 2\end{array}$

Find the value of y, if mean of the given distribution is $40.$

$\begin{array}{cccccc}Age \left(xi\right)& 10& 20& 30& 40& 50\\ Frequency\left(fi\right)& 3& 2& 4& 5& x\end{array}$

Find the value of $x,$ if the mode of the following data is $60.$

$10,60,20,30,20,60,10,50,10,60,30,60,10,20,40,x$

Find the median of the following data:

$5,7,5,6,7,6,7,8,8,9,10,9,5,7,10$

Find the median of the following data:-

$5,7,3,4,5,7,7,3,4,1,2,6,2,7,5$

Find the mode of the folowing distribution:

$300,305,300,306,305,304,305,305,303,305$

Find the mode of the following data:

$15,17,15,16,15,20,15,17,20,16,15,17,16,15$

Find the mode of the following data:

$110,115,110,120,115,120,130,115,110,130,110$

Following table shows the height of $13$ students.

$\begin{array}{cccccc}Height(in cm)& 160& 165& 162& 168& 170\\ No. of students& 3& 4& 3& 2& 1\end{array}$

Find the mean height of the students.

Which one of the following averages can be the best average in the following data :
$391, 384, 591, 407, 675, 522, 777, 753, 2488, 1490$

Mean of six observations $30, 68, 72, 53, 87$and $x$is $60$. Find the value of $x$.

What is the mean of the marks scored by students in a science exam?

$41, 39, 52, 48, 54, 62, 46, 52, 40, 96, 42, 40, 98, 60, 52$.

The mean of the data $8, 0, 3, 3, 1, 7, 4, 1, 4, 4$ is:

If the mean of $m$ observations out of $n$observations is $n$ and the mean of remaining observations is $m$, then what is the mean of all $n$ observations?

The mean of 20 observations is 17. On checking it was found that the two observations were wrongly copied as 3 and 6. If wrong observations are replaced by correct values 8 and 9, then what is the correct mean ?

If the mean age of combined group of boys and girls is 18 years and the mean of age of boys is 20 and that of girls is 16, then what is the percentage of boys in the group ?

The average score obtained by 100 students was 40, but on checking the calculation, it was found that a student's number has been accidentally written 83 in place of 53. What was the actual average obatained by these students?

Find out the mean of mode, median and range of the given data.

$2, 1, 2, 3, 3, 6, 4, 8, 14, 9, 4, 8, 4$