Marks : | Below 10 | Below 20 | Below 30 | Below 40 | Below 50 |
Number of Students : | 3 | 12 | 27 | 57 | 75 |
The frequency table is obtained as follows: \[ \begin{array}{|c|c|} \hline \text{Class Interval (Marks)} & \text{Frequency (Number of Students)} \\ \hline 0 - 10 & 3 \\ 10 - 20 & 9 \\ 20 - 30 & 15 \\ 30 - 40 & 30 \\ 40 - 50 & 18 \\ \hline \end{array} \] The modal class is the class with the highest frequency. From the table, the highest frequency is 30, corresponding to the class interval $30 - 40$.
Let the Mean and Variance of five observations $ x_i $, $ i = 1, 2, 3, 4, 5 $ be 5 and 10 respectively. If three observations are $ x_1 = 1, x_2 = 3, x_3 = a $ and $ x_4 = 7, x_5 = b $ with $ a>b $, then the Variance of the observations $ n + x_n $ for $ n = 1, 2, 3, 4, 5 $ is