Question

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Answer 1

Solution :

Below is the distribution table of daily pocket allowances :

$\sf{\begin{tabular}{|c|c|c|c|} \cline{1-4} C.I. & f_i & x_i & f_i x_i \\ \cline{1-4} 11 - 13 & 7 & 12 & 84 \\ \cline{1-4} 13 - 15 & 6 & 14 & 84 \\ \cline{1-4} 15 - 17 & 9 & 16 & 144 \\ \cline{1-4} 17 - 19 & 13 & 18 & 234 \\ \cline{1-4} 19 - 21 & f & 20 & 20f \\ \cline{1-4} 21 - 23& 5 & 22 & 110 \\ \cline{1-4} 23 - 25 & 4 & 24 & 96 \\ \cline{1-4} & n = 44 + f & & \sum f_i x_i = 752 + 20f \\ \cline{1 - 4} \end{tabular}}$

Now we have, mean = 18

Now we know that,

$\longmapsto\underline{\boxed{\bold{Mean = \dfrac{\sum f_i x_i}{n} }}} \\\\ \\ \longmapsto\sf 18 = \dfrac{752 + 20f}{44 + f} \\\\ \\ \longmapsto\sf 792 + 18f = 752 + 20f \\\\ \\ \longmapsto\sf 20f - 18f = 792 - 752 \\\\ \\ \longmapsto\sf 2f = 40 \\\\ \\ \longmapsto\sf f = \dfrac{40}{2} \\\\ \\ \longmapsto\underline{\boxed{\bold{f = 20}}} \ \star$

Therefore,

Missing frequency , f = 20.

Answer 2

Given :

• Mean = 18

To Find :

• what is frequency ?

Solution :

Concept :

STEP DEVIATION METHOD:

• Step deviation method is used in the cases where the deviation from the assumed mean 'A' are multiples of a common number.

• If the values of ‘di’ for each class is a multiple of ‘h’ the calculation become simpler by taking ui= di/h = (xi - A )/h

From the table :

• Σfiui = x - 20 ,  

• Σfi = 44 + x  

Let the assumed mean, A = 18,  h = 2

MEAN = A + h ×(Σfiui /Σfi)

Substitute all Values :

18 = 18 + 2[(x - 20)/(44+ x)]

18 - 18 =  2[(x -20)/(44 + x)]

0 =  2 [(x - 20)/(44 + x)]

0 = (x -20)

x = 20

• Hence, the missing frequency is 20 .