Trying to wrap my mind around the intuition of the standard error of the mean is the mission.
I was trying to make a really basic example with simple number to give myself more a sense of what is going on. I take three random sample experimentally. The probability in the population is the same.
s=(sample)
s1: 5, 6, 10, 20, 29
s2: 5, 6, 6, 11, 32
s3: 5, 7, 27, 29, 30
If you make the calculation we should obtain:
m=(mean)
m1: 14
m2: 12
m3: 19,6
v=(variance)
v1 84,4
sd=(standard deviation)
sd1: 9,18
sd2: 10,21
sd3: 11,19
Now,
se=(standard error)
using this formula:
$$\frac{σ^{2}}{N}$$
se1 = 84,4 / 5 = 16,8
or this formula
$$\frac{σ}{√N}$$
se1 = 9,18 / 2,23 = 4,11
Shouldn't the two formula be equal and give the same result?