The mean of a distribution is 48 and the sum of all the frequencies is 50. Find the missing frequencies 𝑥 and 𝑦.

 

Given : sum of all frequencies = 50

i.e ⅀𝑓 𝑖 = 50 ⇒ 8 + 6 + 𝑥 + 11 + 𝑦 = 50 

𝑥 + 𝑦 = 25 

The mean is given as 48.

$\text{ Mean }=a+\frac{\sum f_i{u}_i}{\sum f_i}\times h$

$\begin{array}{r}\Rightarrow 48=45+\frac{2y-11}{50}\times 10\\ \Rightarrow 48-45=\frac{2y-11}{5}\\ 3\times 5=2y-11\\ y=13\end{array}$

Substituting 𝑦 = 13 in 𝑥 + 𝑦 = 25 

⇒ 𝑥 + 13 = 25 

⇒ 𝑥 = 12 

Hence, the missing frequencies 𝑥 and 𝑦 are 13 and 12, respectively.