Measures of Central Tendency

The arithmetic mean of the $5$ consecutive integers starting with$\text{'}s\text{'}$ is $\text{'}a\text{'}$. What is the arithmetic mean of $9$ consecutive integers that start with$s + 2$?

The mean weight of a class of $34$ students is $46.5 \mathrm{kg}$. If the weight of the new boy is included, the mean is rises by $500 \mathrm{g}$. Find the weight of the new boy (in $\mathrm{kg}$).

The average of $5$ consecutive numbers is $n$. What will be the average if the next two numbers are included?

The average of $x, y$ and $z$ is $45$.$x$ is as much more than the average as$y$ is less than the average. Find the value of $z$.

The weight of students$(\mathrm{in} \mathrm{kgs})$ in a class are $25, 27, 29, 32, 30, 28, 26, 31, 35, 41, 34$. Find its median in $\mathrm{kg}$.

The weight of students $(\mathrm{in} \mathrm{kgs})$ in a class are $25, 27, 29, 32, 30, 28, 26, 31, 35, 41, 34$. Find its median.

If $\overline{x}$ represent the mean of $n$ observations $x_1,x_2,\dots ,x_n,$ then find the value of $\sum _{i=1}^n\left(x_i-\overline{x}\right)$.

There are $7$ observations in the data and their mean is $11$. If each observation is multiplied by $2$, then the mean of new observations is

Find the mode of the following data.

$7.5, 7.3, 7.2, 7.2, 7.4, 7.7, 7.7, 7.5, 7.3, 7.2, 7.6, 7.2$

Find the median of the scores $75, 21, 56, 36, 81, 05, 42$

The runs scored in $10$ innings by a batsman are $60, 62, 56, 64, 0, 57, 33, 27, 9$ and $71$, respectively. Find the arithmetic mean of the runs scored by him in these innings.

Numbers $50, 42, 35, 2x + 1, 2x - 7, 12, 11, 8, 6$ are arranged in descending order. If their median is $25$, find $x$.

Fifteen students secured the following marks in a test in mathematics. Find the median marks.

$17, 13, 28, 35, 20, 30, 19, 29, 23, 29, 10, 11, 18, 17, 25$.

There are $45$ students in a class of which $15$ are girls. The mean marks of all the girls is $40$ and that of all boys is $47$. Find the mean marks of the entire class rounded off to two decimal places.

Find the median of the following observations :

$87, 64, 46, 77, 41, 58, 90, 35, 55, 92, 33$. If $92$ is replaced by $99$ and $41$ by $43$ in the above data, find the new median.

The mean of $5$ numbers is $18$. If one number is excluded, their mean is $16$. Find the excluded number.

The weights $(\mathrm{in} \mathrm{kg})$ of $10$ newborn babies in a hospital on a particular day are $3.4, 3.6, 4.2, 4.5, 3.9, 4.1, 3.8, 4.5, 4.4$ and $3.6$. Find the mean weight in kilograms.

The median of the observations $11, 12, 14, 18, x+2, x+4, 30, 32, 35, 41$ arranged in ascending order is $24$. Find the value of $x$.

Find the median of daily wage, if the daily wages of workers are (Rs.) $156, 189, 221, 138, 198, 170, 170, 172$.

The percentage of marks obtained by the students of a class are $64, 36, 47, 23, 0, 19, 81, 93, 72, 15, 3, 1$. Find their mean rounded off to two places.