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Mathematics

The mean of the numbers 6, y, 7, x, 14 is 8. Express y in terms of x.

Measures of Central Tendency

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Answer

Arithmetic mean (A.M.) = Sum of termsNo. of terms=xin\dfrac{\text{Sum of terms}}{\text{No. of terms}} = \dfrac{∑x_i}{n}

8=6+y+7+x+1458=x+y+27540=x+y+27x+y=13y=13x.\therefore 8 = \dfrac{6 + y + 7 + x + 14}{5} \\[1em] \Rightarrow 8 = \dfrac{x + y + 27}{5} \\[1em] \Rightarrow 40 = x + y + 27 \\[1em] \Rightarrow x + y = 13 \\[1em] \Rightarrow y = 13 - x.

Hence, the value of y = 13 - x.

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