GATE 2024 DA Q.34: solution and answer

Official answer: 42Source: Official answer key, GATE 2024 DA (IISc Bengaluru)

1. The sample average of 50 points is 40, so the sum of the 50 points is $50\times 40=2000$.

2. Adding the new point 142 gives a new sum of $2000+142=2142$ over $51$ points.

3. The updated mean is ${\bar{x}}_{\text{new}}=\frac{2142}{51}$.

4. Since $51\times 42=2142$, the updated mean is $42$.

5. Check with the update formula ${\bar{x}}_{\text{new}}=\bar{x}+\frac{x_{\text{new}}-\bar{x}}{n+1}=40+\frac{142-40}{51}=40+\frac{102}{51}=42$.