question_answer

Given below is the distribution of weekly pocket money received by students of a class. Calculate the pocket money that is received by most of the students.
Pocket Money (in Rs.)	0 ? 20	20 ? 40	40 ? 60	60 ? 80	80 ? 100	100 ? 120	120 ? 140
No. of Students	2	2	3	12	18	5	2

Answer:

Pocket Money (in Rs.)	Number of Students
0 ? 20	2
20 ? 40	2
40 ? 60	3
60 ? 80	12            \[{{f}_{0}}\]
80 ? 100	18            \[{{f}_{1}}\]    (Maximum)
100 ? 120	5             \[{{f}_{2}}\]
120 ? 140	2
Maximum frequency is 18
\[\therefore \]Modal class\[=80-100\]
Mode \[=l+\frac{{{f}_{1}}-{{f}_{0}}}{2{{f}_{1}}-{{f}_{0}}-{{f}_{2}}}\times h\]
\[=80+\frac{18-12}{36-12-5}\times 20\]
\[=80+\frac{6}{19}\times 20\]
\[=80+\frac{120}{19}=80+6.32\]
\[=86.32\] (approx.)
\[\therefore \] Required pocket money = Rs. 86.32 (approx.)