why is the average value are better than individual values?

Answer 1

When you repeat a measurement several times and then take the average value - you are averaging not only the measurement itself but the error margin aswell; this is much preferred to only taking one measurement.

Answer 2

Statistically, if a measurement varies with a standard deviation (root mean square error or width of curve) sigma, then the average of N measurements varies normally with a standard deviation: sigma / sqrt (N)

So if you take N measurements, the standard deviation of the average is sqrt (N) times smaller than that of one measurement.

Of course this process only reduces random fluctuations between measurements, not systematic errors. For example, if you were measuring length and the true length were just below a measurement line, you might SYSTEMATICALLY overmeasure the length. Another systematic error would be if the zero point were mismarked somehow. Averaging to improve your statistics does not touch such systematic error.

Another good example is polling. If you can get a random sample of 1000 people, you can get a very good read on their average opinion. The more people you ask, the better your estimate. But if there are systematic errors in your survey (like you only include people who own phones and choose to answer your survey), averaging will not fix that.

Answer 3

Typically, such as in a bell-shaped curve, half are higher, and half are lower. It can differ other distributions, but *someone* has to be below average if there's any variation at all. Everyone knows a Back Row Larry.

Answer 4

Anything is possible (individual values)

BUT

What is most likely (averages) is information that can be put to better use.
.

Answer 5

It's symetric to quantum law on our scale.

"Anything can happen."

But by repeating the process over and over, what becomes apparent is what is most likely to happen.