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Mathematics

The mean of following numbers is 68. Find the value of 'x'. 45, 52, 60, x, 69, 70, 26, 81 and 94. Hence, estimate the median.

Measures of Central Tendency

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Answer

Sum of observations = 45 + 52 + 60 + x + 69 + 70 + 26 + 81 + 94 = 497 + x

No. of observations (n) = 9

Mean = Sum of observationsNo. of observations\dfrac{\text{Sum of observations}}{\text{No. of observations}}

68 = 497+x9\dfrac{497 + x}{9}

612 = 497 + x

x = 612 - 497 = 115.

Here, n = 9, which is odd.

Median = n+12\dfrac{n + 1}{2} th term

= 9+12=102\dfrac{9 + 1}{2} = \dfrac{10}{2}

= 5th term

= 69.

Hence, mean = 115 and median = 69.

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