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EEJ MAIN Mathematics QUESTION #7440
Question 1
All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 10 to each of the students. Which of the following statistical measures will not change even after the grace marks were given?
  • mean
  • median
  • mode
  • variance✔️
Correct Answer Explanation
When a constant is added to all observations, the mean, median, and mode all increase by that constant. However, variance (and standard deviation) measure the spread of data around the mean. Since all values shift by the same amount, the spread remains unchanged. Therefore, variance does not change when grace marks are added uniformly to all students.