Is variance only for normal distribution?
Your question is a little vague, but no, variance isn’t used because of its association with the normal distribution. Most distributions have at least a mean and a variance. The same is true if you calculate a standard deviation for a distribution that does not have one.
How do you define a non-normal distribution?
Normal Distribution is a distribution that has most of the data in the center with decreasing amounts evenly distributed to the left and the right. Non-normal Distributions Skewed Distribution is distribution with data clumped up on one side or the other with decreasing amounts trailing off to the left or the right.
What makes a distribution a non-normal distribution?
A non-normal distribution is any distribution of any kind other than normal. Most commonly in practice we find distributions are non-normal because they have a skew (a longer tail on the right or left side), though double-humped distributions and so on are also possible.
What does standard deviation tell us in non-normal?
With median then it makes a sense to talk about quantiles, which could be a way to go with skewed distributions. OP didn’t focus on skewed distributions though. So, for any symmetrical distribution you have mean=median, it doesn’t have top be normal.
Is the calculated mean wrong for non-normally distributed data?
However if the samples are sufficiently large the Central Limit Theorem which guarantees approximate normal distribution for the mean can be applied for the adoption of parametric methods. The calculated mean and the standard deviation are not wrong for non-normal distributed data, nor do they lead to wrong results, as you wrote.
How to transform data into a normal distribution?
Transform the data into normal distribution ¶ The data is actually normally distributed, but it might need transformation to reveal its normality. For example, lognormal distribution becomes normal distribution after taking a log on it. The two plots below are plotted using the same data, just visualized in different x-axis scale.