Question

The question in the textbook says:

"One study mentioned in an article that 90% of the students scored above the national average on standardized tests. Using your knowledge on mean, median and mode, explain why the school reports are incorrect. Does your analysis change if the term "average" refers to mean? To median? Explain what effect this misinformation might have on the perception of the nation's schools."

I really do not know how to answer this question, please help.

Answer 1

Mean is affected by outliers, whereas median is not affected by outliers. So, if the distribution of scores of students is nearly symmetrical, both mean as well as median are proper measures of Central Tendency. Thus, if the distribution of scores of students is nearly symmetrical, the observation that 90% of the students scored above the national average on standardized tests is correct and there is no misinformation that might have on the perception of the nation's schools.

If the distribution of scores of students is not nearly symmetrical, i.e., in the case of skewed distribution, if the term "average" refers to mean, the observation that 90% of the students scored above the national average on standardized tests is incorrect and there is misinformation that might have on the perception of the nation's schools.

However, if the term "average" refers to median, the observation that 90% of the students scored above the national average on standardized tests is correct and there is no misinformation that might have on the perception of the nation's schools.