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The AM of 10 numbers is 20, AM of 30 numbers is 60. AM of combined data is …………A) 40 B) 12 C) 13 D) 50

Answer»

Correct option is: D) 50

AM (Algebraic mean) of 10 numbers is 20.

\(\therefore\) Sum of 10 numbers = \(n_1\overline x_1 = 10 \times 20 = 200\)

AM (Algebraic mean) of 30 numbers is 60.

\(\therefore\) Sum of 30 numbers = \(n_2\overline x_2 = 30 \times 60 = 1800\)

\(\therefore\) AM of combined data is \(\overline x\) = \(\frac {n_1\overline x_1+ n_2\overline x_2}{n_1+n_2}\) 

 =\( \frac {200 + 1800}{10 + 30} = \frac {2000}{40} = 50\)

Hence, algebraic mean (AM) of combined data is 50.

Correct option is: D) 50



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