A distribution consists of 3 components with frequencies 45, 40 and 55 having their means 2, 2.5 and 2 respectively. What is the mean of the combined distribution?

Explanation

Combined mean = \frac{n_1m_1 + n_2m_2 + n_3m_3}{n_1 + n_2 + n_3} = \frac{45 \times 2 + 40 \times 2.5 + 55 \times 2}{45 + 40 + 55} = \frac{90 + 100 + 110}{140} = \frac{300}{140} \approx 2.14.

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