why we need statistics

from rightwingprof, one of the most succinct & clear statements I've seen:

Before I go on, let me quickly address why we must analyze the data statistically, and cannot just report means. If we gave the same kids the same proficiency exams on two different days, say only a week apart, their scores would be different. Anytime we see a difference between scores, without statistics, we do not know if those differences are due to random variation or not. We cannot without statistics point to two different scores or means and say, "See? The scores increased!"

Also, let me mention a few crucial points.

• The more data we have, the more reliable our statistical analysis will be (this will become an issue later on).
  

• Means (averages) alone do not give us a complete picture, particularly when they are means of aggregated data, as these are (this is why I look at other descriptive statistics).
  

• Statistics always deals with probability (uncertainty), and we calculate our statistics to a specific probability, 95% here (sometimes statistics are calculated to a 99% probability). This is the level of sensitivity (alpha), here, 0.05.
  

• We are assuming here either that the proficiency exam standards did not change between the two years or that the proficiency reports for the two years are comparable (if they are not, then Wisconsin cannot make any statement about their proficiency levels over time).