The average weight of $8$ persons increases by $2.5\, kg$ when a new person comes in place of one of them weighing $65\, kg$. What might be the weight of the new person? (in $kg$)

The average age of board of directors of a company, having $10$ directors was $48$ years. Coincidentally when a director aged $53$ resigned from the board of directors, another director died on the same day. So a new director joined the board of directors aged $34.$ Next year in the same month the average age of all the $9$ directors was found to be $46 \,years.$ The age of the late (i.e., dead) director at the time of his death was (in $years$)

The mean of $19$ observations is $4 .$ If one more observation of $24$ is added to the data, the new mean will be

The average height of the students of a class of $20$ is $105\, cm$. If ten more students of average height of $120 \,cm$ join this class, the average height of the class will become (in $cm$)

A student was asked to find the arithmetic mean of the numbers $3,11,7,9,15,13,8,19,17,21,14$ and $x$. He found the mean to be $12 .$ What should be the number in place of $x ?$