Find the missing frequency (x) of the following distribution, if mode is 34.5: | |||||
Marks obtained | 0 ? 10 | 10 ? 20 | 20 ? 30 | 30 ? 40 | 40 ? 50 |
Number of students | 4 | 8 | 10 | x | 8 |
Answer:
C.I. Frequency 0 ? 10 4 10 ? 20 \[8={{f}_{0}}\] l = 20 ? 30 \[10={{f}_{1}}\] 30 ? 40 \[x={{f}_{2}}\] 40 ? 50 8 Mode \[=l+\left( \frac{{{f}_{1}}-{{f}_{0}}}{2{{f}_{1}}-{{f}_{0}}-{{f}_{2}}} \right)h\] \[34.5=20+\left( \frac{10-8}{20-8-x} \right)10\] \[\Rightarrow \] \[34.5=20+\left( \frac{2}{12-x} \right)10\] \[\Rightarrow \] \[\frac{14.5}{1}=\frac{20}{12-x}\] \[\Rightarrow \] \[20=14.5(12-x)\] \[\Rightarrow \] \[\frac{20}{14.5}=12-x\] \[\Rightarrow \] \[\frac{40}{29}=12-x\] \[\Rightarrow \] \[x=12-\frac{40}{29}\] \[\Rightarrow \] \[x=\frac{348-40}{29}\] \[\Rightarrow \] \[x=\frac{308}{29}\] \[\Rightarrow \] \[x=10.62\]
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