Option 1 : 45.18

Given:

The average marks of 50 students are 45

A wrong entry of 23 marks instead of 32 marks

Formula used:

Average = Sum of observations/Total number of observations

Calculation:

According to the question,

Total marks of the student = 45 × 50 = 2250

It was found that a wrong entry of 23 marks instead of 32 marks.

⇒ After correction the total marks of student = 2250 - 23 + 32

⇒ After correction the total marks of student = 2259

Now, the correct average = 2259/50 = 45.18.

∴ The correct average is 45.18.

⇒ The difference between wrong entry and correct one = 32 - 23 = 9

⇒ The increase in average marks = 9/50 = 0.18

⇒ The correct average = 45 + 0.18 = 45.18.

∴ The correct average is 45.18