NIMCET 2022 — Mathematics PYQ

Step-by-step Solution 
1. Calculate the original sum of observations: 
The mean of $25$ observations was found to be $38$. The sum of observations is calculated as $\text{Mean}\times \text{Number of observations}$. Original sum $=38\times 25=950$. 

1. Adjust the sum for misread values: 

It was discovered that $23$ and $38$ were misread as $25$ and $36$. To find the correct sum, the misread values must be subtracted and the correct values must be added. Correct sum $=\text{Original sum}-(\text{Misread value }1+\text{Misread value }2)+(\text{Correct value }1+\text{Correct value }2)$. Correct sum $=950-(25+36)+(23+38)$. Correct sum $=950-61+61$. Correct sum $=950$. 
1. Calculate the correct mean: 

The correct mean is found by dividing the correct sum by the number of observations. Correct mean $=\frac{\text{Correct sum}}{\text{Number of observations}}$. Correct mean $=\frac{950}{25}$. Correct mean $=38$. [1, 2]  
Final Answer 
The final answer is $\boxed{\text{38}}$.