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Mathematics

Find the mean of 25 given numbers when the mean of 10 of them is 13 and the mean of the remaining numbers is 18.

Measures of Central Tendency

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Answer

Arithmetic mean (A.M.)=Sum of termsNo. of termsSum of terms=A.M.×No. of terms.\text{Arithmetic mean (A.M.)} = \dfrac{\text{Sum of terms}}{\text{No. of terms}} \\[1em] \therefore \text{Sum of terms} = \text{A.M.} \times \text{No. of terms}.

Given, mean of 10 numbers is 13.

∴ Sum of 10 terms = 13 × 10 = 130.

Given, mean of 15 numbers is 18.

∴ Sum of 15 terms = 15 × 18 = 270.

Sum of 25 terms = 130 + 270 = 400.

A.M.=40025=16\therefore A.M. = \dfrac{400}{25} = 16

Hence, the mean of 25 numbers is 16.

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