Brian the Brain
In an elementary classroom, the scores among all the students are normally distributed.
Then there comes a new student, Brian, who is exceptionally brilliant and scores 100% on all exams, clearly exceeding his class mates' average.
Which of the following will be the result of the new distribution after Brian's arrival?
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1 solution
In a normal bell-shaped distribution, the data are evenly scattered over variance range and will have the mean = median = mode.
In case of skewness, however, the normal distribution is disturbed with a group of extremely variant data either over the original median (thus named right-skew) or below (thus left-skew).
For Brian's presence, his high scores indeed increase the overall classroom's mean, making the distribution right-skew, while the median always stays in the middle. On the other hand, the mode (highest prevalent scores) drops below the former parameters: the majority of Brian's classmates have lower scores than he does.
As a result, with the right-skew distribution, the mean > median > mode.