Measures of Central Tendency

The mean weight of $150$ students in a certain class is $60 \mathrm{kg}.$ The mean weight of boys is $70 \mathrm{kg}$ and that of girls is $55 \mathrm{kg}.$ What are the number of boys and girls respectively in the class?

A car travels first $60 \mathrm{km}$ at a speed of $3v \mathrm{km}/\mathrm{h}$ and travels next $60 \mathrm{km}$ at $2v \mathrm{km}/\mathrm{h}.$ What is the average speed of the car?

Consider the following discrete frequency distribution.

What is the value of median of the distribution?

The arithmetic mean of $100$ observations is $40.$ Later, it was found that an observation $53$ was wrongly read as $83$. What is the correct arithmetic mean?

The median of the observations $22$ $24, 33, 37, x+1, x+3, 46, 47, 57, 58$ in ascending order is $42.$What are the values of $5^{\mathrm{th}} \& 6^{\mathrm{th}}$ observations respectively?

A data set of $n$ observations has mean $2M,$ while another data set of $2n$ observations has mean $M.$ What is the mean of the combined data sets?

The sum of deviations of $n$ number of observations measured from $2.5$ is $50.$ The sum of deviations of the same set of observations measured from $3.5$ is $-50.$ What is the value of $n?$

The numbers $4$ and $9$ have frequencies $x$ and $(x-1)$ respectively. If their arithmetic mean is $6,$ then what is the value of $x?$

Consider the following statements
1. The algebraic sum of deviations of a set of values from their arithmetic mean is always zero.
2. Arithmetic mean $>$ Median $>$ Mode for a symmetric distribution.

Which of the above statements is/are correct?