# Given two sets of data, what could explain similar means but different standard deviations?

Given two sets of data of user activity, both of which appear to be in an exponential distribution, I have calculated the mean and standard deviations using both a mean/deviation and a sample mean/deviation (sample size = 30, number of samples = 10k):

### A (size: 627,000):

• Raw --  μ = 45.947, σ = 114.2, σ/√n = 0.14422

### B (size:3570):

• Raw --  μ = 46.43, σ = 116.1

Using the above data, it seems that the two means differ by a statistically significant amount, and thus allow us to say with confidence that the average for B is greater than the average of A.

### A

• Sampling --  μ = 46.174, σ = 21.256

### B

• Sampling --  μ = 46.786, σ = 21.366

Using the sampling data standard deviations, we see that the difference in means (0.612) is much less than the deviation, it seems that the means do not differ by a statistically significant amount.

So given the above, which is right? Can we say that these data sets differ? If the underlying distribution is exponential, are the above tests even accurate?

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