A data set of n observations has mean 2 x bar while another data set of 2n observations has mean x bar .

Question

A data set of n observations has mean 2\(\overline{x}\) while another data set of 2n observations has mean \(\overline{x}\).The mean of the combined data set of 3n observations will be equal to:

(a) \(\overline{x}\)

(b) \(\frac{3}{2}\)\(\overline{x}\)

(c)  \(\frac{2}{3}\)\(\overline{x}\)

(d)  \(\frac{4}{3}\)\(\overline{x}\)

Answer 1

(d) \(\frac{4}{3}\)\(\overline{x}\)

Mean of the combined data = \(\frac{n\times2\overline{x}+2n\times\overline{x}}{n+2n}\)

= \(\frac{2n\overline{x}+2n\overline{x}}{3n}\) = \(\frac{4n\overline{x}}{3n}=\frac43\overline{x}\)