question_answer

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 \[=l+\left( \frac{{{f}_{1}}-{{f}_{0}}}{2{{f}_{1}}-{{f}_{0}}-{{f}_{2}}} \right)h\]
\[34.5=20+\left( \frac{10-8}{20-8-x} \right)10\]
\[\Rightarrow \]                           \[34.5=20+\left( \frac{2}{12-x} \right)10\]
\[\Rightarrow \]                           \[\frac{14.5}{1}=\frac{20}{12-x}\]
\[\Rightarrow \]                           \[20=14.5(12-x)\]
\[\Rightarrow \]                           \[\frac{20}{14.5}=12-x\]
\[\Rightarrow \]                           \[\frac{40}{29}=12-x\]
\[\Rightarrow \]                           \[x=12-\frac{40}{29}\]
\[\Rightarrow \]                           \[x=\frac{348-40}{29}\]
\[\Rightarrow \]                           \[x=\frac{308}{29}\]
\[\Rightarrow \]                           \[x=10.62\]