Question

the mode of the following data is 67 .find the missing frequency
class. frequency

40-50. 5
50-60. x
60-70. 15
70-80. 12
80-90. 7​

Answer 1

GIVEN :-

• Mode = 67

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TO FIND :-

• Missing frequency 'x '

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SOLUTION :-

• Mode = 67

• Modal class = 60 - 70

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$\large \boxed {\underbrace {\underline {\sf {\red { Mode \;= l + \left\{ \dfrac {f_1 - f_0}{2f_1 - f_0 - f_2 } \right\} \times h}}}}}$

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where,

• l = lower limit of modal class, l = 60

• h = class height, h = 50 - 40 = 10

• f_1 = frequency of modal class, f_1 = 15

• f_0 = frequency of preceding modal class, f_0 = x

• f_2 = frequency of succeeding modal class, f_2 = 12

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Now,

$\small {\underline {\underline {\frak {\green { Substituting \; values \; in \; Formula :}}}}}$

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$: \implies \sf { 67 = 60 + \left\{ \dfrac { 15 - x}{2(15) - x - 12} \right\} \times 10 }$

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$: \implies \sf { 67 -60 = \left\{ \dfrac {15 - x}{18 - x} \right\} \times 10}$

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$: \implies \sf { 7 (18 - x) = (15 - x) 10 }$

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$: \implies \sf { 126 - 7x = 150 - 10x}$

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$: \implies \sf { 10 - 7x = 150 - 126 }$

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$: \implies \sf { 3x = 24 }$

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$: \implies \sf { x=8}$

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$\sf {\underline {\underline { Therefore, \; missing \; frequency \; = 8 \; \checkmark }}}$