Question

find the missing frequances in the
following fraqrance distribution if it is
known that the mean 1.46
x 0 1 2 3 4 5
f 46 ? ? 25 10 5
Total= 200​

Answer 1

Let the missing Frequency be x and y Respectively.

${\sf{ \Sigma f_i = 86 + x + y }} \\ {\sf{And, \Sigma f_i = 200 }} \\ \\ \colon\implies{\sf{ 86+x+y = 200 }} \\ \\ \colon\implies{\sf{ x+y = 200-86 }} \\ \\ \colon\implies{\sf{ x+y = 114 \ \ \ \ \ \ \ \cdots(1) }}$

As we know that:

$\circ \ {\large{\pmb{\underline{\boxed{\sf\pink{ Mean = \dfrac{ \Sigma (f_i \times x_i ) }{ \Sigma f_i } }}}}}} \\ \\ \\ \colon\implies{\sf{ 1.46 = \dfrac{140+x+2y}{86+x+y} }} \\ \\ \\ \colon\implies{\sf{ 1.46 = \dfrac{ 140+x+y+y}{86+x+y} }} \\ \\ \\ \colon\implies{\sf{ 1.46 = \dfrac{ 140+114+y}{86+114} }} \\ \\ \\ \colon\implies{\sf{ 1.46 = \dfrac{ 254+y}{200} }} \\ \\ \\ \colon\implies{\sf{ 1.46 \times 200 = 254 + y }} \\ \\ \\ \colon\implies{\sf{ 292 = 254+y }} \\ \\ \\ \colon\implies{\sf{ y = 292-254 }} \\ \\ \colon\implies{\sf{ y = 38 }}$

Putting y = 38 in Equation (1) to get value of x as:

$\colon\implies{\sf{ x+y = 114 }} \\ \\ \colon\implies{\sf{ x + 38=114 }} \\ \\ \colon\implies{\sf{ x = 114-38 }} \\ \\ \colon\implies{\sf{ x = 76 }}$

Hence,

${\pmb{\underline{\sf{ The \ missing \ Frequency \ are \ 76 \ and \ 38 \ respectively. }}}}$