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Answer 1

Given:-

• A Frequency distribution table is given to us .

To Find :-

• The mean marks .

Solution :-

Given table to us is ,

$\begin{tabular}{|c|c|c|c|c|c|}\cline{1-6} Marks & Below 10&Below 20 & Below 30 & Below 40 & Below 50 \\\cline{1-6} \sf \underset{Studens}{No. \:of} & 8&17&32&62&80\\\cline{1-6} \end{tabular}$

From this table we can prepare a table with class intervals as follows ,

$\begin{tabular}{|c|c|c|c|} \cline{1-4} \bf Class Interval & \bf No. of students & \bf Class Mark & \bf \bf f_ix_i \\\cline{1-4} 0-10 & 8 & 5 & 40 \\\cline{1-4} 10-20 &9&15&135\\\cline{1-4} 20-30 &15&25&375\\\cline{1-4} 30-40 &30&35&1050\\\cline{1-4} 40-50 &18&45&810 \\\cline{1-4} & \sf \Sigma f_i =30 && \sf \Sigma f_ix_i=2410 \\\cline{1-4}\end{tabular}$

Now , we know mean as ;

$=> Mean =\dfrac{\Sigma f_i x_i }{\Sigma f_i}\\=> Mean = \dfrac{2410}{80} \\\bf=> Mean = 30.125$

$\Large\boxed{\pink{\sf \red{\bigstar}Mean = 30.125}}$