# Thread: Simple Statistics

1. ## Simple Statistics

The mean and the standard deviation of the marks of a class in an Exam were 53 and 7 respectively. The test was then given to a new student who scored 63. Which of the following statements is certainly true?

A) The range increased
B) The mean increased
C) The standard deviation increased
D) The median increased

The answer to this question was B,C and D. I know that the mean will increased as the score is higher than the mean, but I don't understand why the standard deviation and the median would CERTAINLY increase?

2. Originally Posted by requal
The mean and the standard deviation of the marks of a class in an Exam were 53 and 7 respectively. The test was then given to a new student who scored 63. Which of the following statements is certainly true?

A) The range increased
B) The mean increased
C) The standard deviation increased
D) The median increased

The answer to this question was B,C and D. I know that the mean will increased as the score is higher than the mean, but I don't understand why the standard deviation and the median would CERTAINLY increase?
Look at the definition of variance and you will see why the variance must increase.

However, I would argue that it's not certain that the median will change (there may be several scores of 63 in the middle ranks ....)