Can you have constant mean across samples with different distributions? Can data samples have constant means even if they are from different distributions?
 A: Sampling usually implies a random element so you are not guaranteed equal means of the samples (i assume this is what you mean by "constant"). But randomness also means that some samples drawn from different distributions will have equal means.
To be more precise:


*

*Continuous vs. discrete: Samples from continuous distributions have infinitesimal probability of having equal means while the chances are better from discrete distributions. 

*Probability of outcome: For distributions with discrete outcomes, a very high probability of one of the outcomes increases the chances that the samples will be identical.

*Sample size: Large samples sizes decrease probability of EQUAL means for equal discrete distributions and for all different distributions. They increase the probability of getting SIMILAR means (i.e. not exactly equal but close) for all equal distributions.


E.g. in R:
# These two different (discrete) Bernoulli samples are very likely to have equal means, i.e. 1
rbinom(n=5, size=1, prob=0.999)  # 5 samples with 99,9% chance of being 1
rbinom(n=5, size=1, prob=0.998)  # 5 samples with 99,8% chance of being 1

# These two are very likely to be different (big sample size) even though they're from the same distribution
rbinom(n=1000, size=1, prob=0.5)  # 1000 samples with 50% probability of being 1
rbinom(n=1000, size=1, prob=0.5)  # 1000 samples with 50% probability of being 1

#These two are almost guaranteed to be different, because they are continuous, even though the sample size is small
rnorm(2, mean=0, sd=1)  # two samples from the standard normal distribution
rnorm(2, mean=0, sd=1)  # two samples from the standard normal distribution

A: No two samples will have exactly the same mean, even if they are from the same distribution. But, if you mean approximately the same, certainly, why not?
e.g
set.seed(123) #Set the seed
xnorm <- rnorm(100, 0, 1) #Normally distributed
xunif <- runif(100, -1,1) #Uniformly distributed
mean(xnorm)
mean(xunif)

These aren't exactly the same, because of sampling error; you can make them closer by increasing sample size.
