Find the value of, the missing frequency, If the mean of the following distribution is 67.
Class Interval
Frequency
25-35
10
35-45
6
45-55
4
55-65
f
65-75
4
75-85
12
85-95
26
Mean is 23.71
If true then enter $1$ and if false then enter $0$

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Solution

$F o r g r o u p e d d a t a w h e n C l a s s I n t e r v a l i s g i v e n, w e f i n d t h e C l a s s M a r k . C l a s s M a r k = m i d p o i n t o f a n i n t e r v a l = \frac{(L o w e r l i m i t + U p p e r l i m i t)}{2} C l a s s M a r k i s t a k e n a s x_{i} f o r e a c h c l a s s i n t e r v a l . F i n d x_{i} f_{i} . F r o m t h e t a b l e, w e h a v e Σ x_{i} f_{i} = 4320 + 60 f & Σ f_{i} = 62 + f G i v e n M e a n = 67 M e a n = \frac{Σ x_{i} f_{i}}{Σ f_{i}} \Rightarrow 67 = \frac{4320 + 60 f}{62 + f} \Rightarrow (62 + f) \times 67 = 4320 + 60 f \Rightarrow 4154 + 67 f = 4320 + 60 f \Rightarrow 67 f - 60 f = 4320 - 4154 \Rightarrow 7 f = 166 \Rightarrow f = \frac{166}{7} \Rightarrow f = 23.71$

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