# Resolved: Uniform distribution and CLT?

Not seeing how uniform distribution can work with sample means and CLT. If a uniform distribution has equal probability along its distribution, how can taking sample means end up with a normal distribution?

1 answers ( 1 marked as helpful)

Hey Thomas,

Even though a uniform distribution has equal chances for every value within its range, the Central Limit Theorem (CLT) tells us something interesting - when you start taking the average of a large number of samples from that uniform distribution, the averages will begin to form a bell-shaped curve, or a normal distribution.

So, even if the original data is spread out evenly, when you take many samples and average them, those averages start looking more and more like a normal distribution. It’s one of the fascinating ways that randomness and probability work together!

So, even if the original data is spread out evenly, when you take many samples and average them, those averages start looking more and more like a normal distribution. It’s one of the fascinating ways that randomness and probability work together!

Essentially, it is much likelier to draw the mean than the extremes and this is why we end up with a normal distribution.

Best,

Ned