Find the missing frequency x of the following distribution- if mode is 24-5 -Wline t e x t M a r k s o b t a i n e d - 0-10 - 10-20 - 20-30 - 30-40 - 40-50 1WlineWlinelend array

[ C.I. amp; Frequency; 0 10 amp; 4; 10 20 amp; 8 = f_0; l = 20 30 amp; 10 = f_1; 30 40 amp; x = f_2; ...

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Standard X

Mathematics

Mode

Find the miss...

Question

Find the missing frequency (x) of the following distribution, if mode is 24.5:

$\begin{matrix} Marks obtained & 0 - 10 & 10 - 20 & 20 - 30 & 30 - 40 & 40 - 50 Number of students & 4 & 8 & 10 & x & 8 \end{matrix}$

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Solution

$\begin{matrix} C.I. & Frequency 0 - 10 & 4 10 - 20 & 8 = f_{0} l = 20 - 30 & 10 = f_{1} 30 - 40 & x = f_{2} 40 - 50 & 8 \end{matrix}$
$M o d e = l + (\frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}}) h 24.5 = 20 + (\frac{10 - 8}{20 - 8 - x}) 10 \Rightarrow 24.5 = 20 + (\frac{2}{12 - x}) 10 \Rightarrow \frac{4.5}{1} = \frac{20}{12 - x} \Rightarrow 20 = 4.5 (12 - x) \Rightarrow \frac{20}{4.5} = 12 - x \Rightarrow \frac{40}{9} = 12 - x \Rightarrow x = 12 - \frac{40}{9} \Rightarrow x = \frac{108 - 40}{9} \Rightarrow x = \frac{68}{9} \Rightarrow x = 7.57$

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Find the missing frequency (x) of the following distribution, if mode is 24.5: Marks obtained0−1010−2020−3030−4040−50Number of students4810x8

C.I.Frequency0−10410−208=f0l=20−3010=f130−40x=f240−508 Mode=l+(f1−f02f1−f0−f2)h24.5=20+(10−820−8−x)10⇒24.5=20+(212−x)10⇒4.51=2012−x⇒20=4.5(12−x)⇒204.5=12−x⇒409=12−x⇒x=12−409⇒x=108−409⇒x=689⇒x=7.57

Find the missing frequency (x) of the following distribution, if mode is 24.5:

$\begin{matrix} Marks obtained & 0 - 10 & 10 - 20 & 20 - 30 & 30 - 40 & 40 - 50 Number of students & 4 & 8 & 10 & x & 8 \end{matrix}$