If ${d_i}$ is the deviation of a class mark ${y_i}$ from $a$,the assumed mean,and ${f_i}$ is the frequency,if ${M_g} = x + \frac{1}{{\sum {f_i}}}(\sum {f_i}{d_i})$,then $x$ is:

Consider a set of observations ${x_1}, {x_2}, {x_3}, ..., {x_{101}}$ such that ${x_1} < {x_2} < {x_3} < ... < {x_{100}} < {x_{101}}$. The mean deviation of this set of observations about a point $k$ is minimum when $k$ equals:

$A$ school has four sections of chemistry in class $XII$ having $40, 35, 45$ and $42$ students. The mean marks obtained in chemistry test are $50, 60, 55$ and $45$ respectively for the four sections. The overall average of marks per student is:

The number of observations in a group is $40$. If the average of the first $10$ observations is $4.5$ and the average of the remaining $30$ observations is $3.5$,then the average of the whole group is:

The median of a set of $9$ distinct observations is $20.5$. If each of the largest $4$ observations of the set is increased by $2$,then the median of the new set:

The relation between the median $M$,the second quartile ${Q_2}$,the fifth decile ${D_5}$,and the $50^{th}$ percentile ${P_{50}}$ of a set of observations is: