Question

A distribution consists of three components with frequencies 45 ,40 and 15 having their means 2,2.5 and 2 respectively . find combined mean

Answer 1

Solution: A distribution consists of three components with frequencies 45 ,40 and 15 having their means 2,2.5 and 2 respectively . find combined mean

Answer: Let $\bar{x_{1}}$ be the mean of first component and $n_{1}$ be the frequency of first component

Let $\bar{x_{2}}$ be the mean of second component and $n_{2}$ be the frequency of second component

Let $\bar{x_{3}}$ be the mean of third component and $n_{3}$ be the frequency of third component

Then we have:

$\bar{x_{1}} = 2, n_{1} = 45$

$\bar{x_{2}} = 2.5, n_{2} = 40$

$\bar{x_{3}} = 2, n_{3} = 15$

Now the combined mean is:

Combined mean $=\frac{\bar{x_{1}} \times n_{1}+\bar{x_{2}} \times n_{2}+\bar{x_{3}} \times n_{3}}{n_{1} +n_{2} +n_{3}}$

                            $=\frac{2 \times 45 +2.5 \times 40 +2 \times 15}{45+40+15}$

                            $=\frac{90 + 100 + 30}{100}$

                            $=\frac{220}{100}=2.2$

Therefore, the combined mean is 2.2