The irregularities and noise in the data we've discussed above come from different 
sources.  Scientists call this "extra" information ERROR, because it would lead 
you to incorrect results if you took it literally without analyzing the data 
statistically.  Error is classified into two broad categories.

RANDOM ERROR occurs for each measurement in a data set.  Every time you obtain a 
data point, it could be off target for a wide variety of largely unpredictable 
reasons.  Imagine, for example, trying to draw 100 lines on a sheet of paper, each 
exactly one inch long.  Each line will be close to an inch, but will be longer or 
shorter depending on a myriad of microscopic muscle movements - sufficiently 
unpredictable that the amount of error on each line is pretty much random.

SYSTEMATIC ERROR occurs for every measurement in a data set.  This happens if the 
measuring equipment is flawed - for example, if a ruler marked as 12 inches long 
is actually only 11 inches long, or if a lamp is left on in a telescope dome.  It 
can also happen if the experiment designed to gather the data is flawed, and 
doesn't measure a fair and representative sample - an opinion poll, perhaps, that 
wants to know how all Americans think about a topic, but only asks children by 
accident.

If you reduce the random error of a data set, you reduce the width (FULL WIDTH AT 
HALF MAXIMUM) of a distribution, or the counting noise (POISSON NOISE) of a 
measurement.  Usually, you can reduce random error by simply taking more 
measurements.  Imagine a not-very-accurate archer shooting arrows at a given spot 
on a wall.  If you use his first 3 shots as a guide, you may not know where he's 
aiming; but if you use his first 50 shots, there's a good chance that the 
distribution will be centered around the spot.

To reduce the systematic error of a data set, you must identify the source of the 
error and remove it.  Unfortunately, unless you do that, you will never reduce the 
systematic error by taking more measurements.  If our archer friend consistently 
aims to the left of the spot he wants to hit, his arrows will cluster around the 
wrong place; no matter how many shots he takes, we'll arrive at the wrong 
conclusion unless he corrects the systematic left-ness of his aim.