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.)
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