Question

If the combined mean of two groups is $\frac{40}{3}$ and if the mean of one group with $10$ observations is $15$, then the mean of the other group with $8$ observations is equal to

• A. $\frac{46}{3}$
• B. $\frac{35}{4}$
• C. $\frac{45}{4}$
• D. $\frac{41}{4}$
• E. $\frac{43}{4}$

Answer 1

Answer: (C)

Let ${\bar{x}}_1$ and ${\bar{x}}_2$ be the mean of the two observations with $n_1=10$ and $n_2=8$. Then, their combined mean $\bar{X}$ can be given as
$\bar{X}=\frac{n_1{\bar{X}}_1+n_2{\bar{X}}_2}{n_1+n_2}$
$\Rightarrow \frac{40}{3}=\frac{10\times 15+8\times {\bar{x}}_2}{10+8}$
$\Rightarrow \frac{40}{3}=\frac{150+8{\bar{x}}_2}{18}$
$\Rightarrow {\bar{x}}_2=\frac{45}{4}$