GATE DA 2024 | Question 34
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 ______.
Explanation
Answer: 42
The average gives the total: 50 points with mean 40 add up to \(50 \times 40 = 2000\). With the new point the total is \(2000 + 142 = 2142\) over 51 points, so the new mean is
\[\frac{2142}{51} = 42.\]
A quick check: the new point lies \(142 - 40 = 102\) above the old mean, and that excess is shared by all 51 points, raising the mean by \(102/51 = 2\). Dividing by 50 instead of 51 is the usual slip.
Answer: 42