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GATE DA 2024 Q34: Updated sample mean after adding one data point

Question

The sample average of 50 data points is 40. The updated sample average after including a new data point taking the value of 142 is ______.

Try it: numerical answer: type the value

Numerical answer. No negative marking.
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Answer: 42 (official GATE 2024 final answer key)

Concept used: Running mean: new mean =nxˉ+xnewn+1= \dfrac{n\bar{x} + x_{new}}{n+1}.

First step: The sum of the 50 points is 2000; add 142 and divide by 51.

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Source: official GATE 2024 DA question paper and final answer key, organised by IISc Bangalore. Question paper · Answer key