1.

The mean of 10 numbers is 7. The mean of 15 numbers is 12 then the mean of all observations is ………… A) 9 B) 10 C) 12 D) 11

Answer»

Correct option is: B) 10

Given that the mean of 10 numbers is 7.

\(\therefore\) Sum of these 10 observations = \(n_1\overline x_2\)= 10 \(\times\)7 = 70

Also given that the mean of 15 numbers is 12.

\(\therefore\) Sum of these 15 observations =  \(n_2\overline x_2\)= 15 \(\times\)12 = 180.

There are total 10 + 15 or 25 observations whose sum are \(n_1\overline x_2\) + \(n_2\overline x_2\) = 70 + 180 = 250

\(\therefore\) Mean of all observations = \(\frac {Sum \, of\, all\, obs.}{Total\, No\, of \,obs}\) = \(\frac {n_1\overline x_2 + n_2\overline x_2}{n + n_2}\)

=  = \(\frac {70 + 180}{10 + 15} = \frac {250}{25} = 10\)

Hence, mean of all observations is 10.

Correct option is: B) 10


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