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The mean of a data set comprising of 16 observations is maximum value of $x^{3} + 4 x + 5 in [- 1, 2]$ . If one of the observations valued 16 is deleted and three new observations valued 3, 4 and 5 are added to the data, then the mean of the resultant data is ________

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answer is 14.

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Detailed Solution

Maxi : value of $x^{3} + 4 x + 5 in [- 1, 2] is 16$

$\frac{\sum_{i = 1}^{15} x_{i} + 16}{16} = 16 \Rightarrow \sum_{i = 1}^{15} x_{i} = 240$

$∴ required mean \frac{\sum_{i = 1}^{15} x_{i} + 3 + 4 + 5}{18} = 14$

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