Question

answer it please...........​

Answer 1

GiveN :-

• A Cummulative Frequency Table is given to us.
• The total number of students is 100 .

To FinD :-

• The mean marks of the Class.

AnsweR :-

$\underline{\red{\sf Given\ table\ to\ us\ is :- }}$

$\begin{tabular}{|c|c|}\cline{1-2} \bf Marks & \bf No. of students \\\cline{1-2} \sf Less than 50 & \sf 8 \\\cline{1-2} \sf Less than 100 & 23 \\\cline{1-2} \sf Less than 150 & \sf 55 \\\cline{1-2} \sf Less than 200 & \sf 81 \\\cline{1-2} \sf Less than 250 & \sf 93 \\\cline{1-2} \sf Less than 300 & \sf 100 \\\cline{1-2}\end{tabular}$

This distribution given above is called the " Cummulative Frequency Distribution of Less than type . "

The table is in form of Less than 50 , Less than 100 ..... Less than 300. We can make class intervals as 0- 50 , 50 - 100 ........... , 250 - 250 . We can find the frequencies of the respective class intervals by subtracting the Cummulative Frequencies .

$\underline{\red{\sf Hence \ we \ can \ make \ new \ Table \ as :- }}$

$\boxed{\begin{tabular}{|c|c|c|c|}\cline{1-4} \bf Class Interval & \bf No. of students & \bf Class Mark & \bf f_i x_i \\\cline{1-4} \sf 0 -50 & \sf 8 & \sf 25 & \sf 120 \\\cline{1-4} \sf 50-100 & \sf 15 & \sf 75 & \sf 1125 \\\cline{1-4} \sf 100-150 & \sf 32 & \sf 125 & \sf 4000 \\\cline{1-4} \sf 150-200 & \sf 26 & \sf 175 & \sf 4,550 \\\cline{1-4} \sf 200 -250 & \sf 12 & \sf 225 & \sf 2700 \\\cline{1-4} \sf 250 -300 & \sf 6 & \sf 275 & \sf 1925 \\\cline{1-4} & \sf \bf \Sigma f_i = 100 & & \bf\Sigma (f_i\times x_i) = 14,420 \\\cline{1-4}\end{tabular}}$

$\underline{\underline{\orange{\textbf{\textsf{ \leadsto Mean \ of\ the\ the\ data\ is\ given\ by\ :- }}}}}$

$\large\qquad\boxed{\purple{\bf \bar{x}=\dfrac{\Sigma f_i x_i }{\Sigma f_i }}}$

$\tt:\implies \pink{ Mean = \dfrac{\Sigma f_i x_i }{\Sigma f_i }} \\\\\tt:\implies Mean = \dfrac{14420}{100}\\\\\underline{\boxed{\red{\tt\longmapsto Mean = 144.20 }}}$

$\boxed{\green{\bf\pink{\dag}\: Hence \ the \ mean \ of \ the \ class \ is \ 144.2 .}}$