Calculate the total marks based on the initial mean:

• Given: Mean = $40$, Number of students = $100$
• Total marks = Mean × Number of students = $40 \times 100 = 4{,}000$

Adjust for the misread mark:

• The mark of 53 was misread as 83.
• Corrected total marks = Total marks - Misread mark + Correct mark
• Corrected total marks = $4{,}000 - 83 + 53 = 3{,}970$

Calculate the corrected mean:

• Corrected mean = Corrected total marks $\div$ Number of students
• Corrected mean = $3{,}970 \div 100 = 39.7$
• Therefore, the corrected mean marks are 39.7.