How Statistics Works
Mean — The Center of Gravity
Where the balance point of a data set lies
The points are moderately spread out. The mean balances the data, but individual points pull it in different directions.
Step 1 of 6: Mean — The Center of Gravity
Where the balance point of a data set lies
The points are moderately spread out. The mean balances the data, but individual points pull it in different directions.
Step 2 of 6: Variance & Standard Deviation
How spread out data is around the mean
Moderate spread. The data fans out enough to show variety but the bell shape keeps most values within a couple of standard deviations of center.
Step 3 of 6: Populations vs Samples
Why samples are noisy estimates of the truth
At n = 30, the sample histogram is starting to resemble the population shape. The sample mean (x̄ = 47.4) is getting closer to the true mean.
Step 4 of 6: The Central Limit Theorem
Sample means always form a bell curve
The bell shape is emerging! At n = 5, the distribution of means is visibly concentrating around 5 with std error ≈ 1.29. The CLT is working.
Step 5 of 6: Confidence Intervals
Quantifying uncertainty in estimates
The 95% level is the standard choice in science. It balances precision and reliability — the z-score of 1.96 captures most of the distribution.
Step 6 of 6: Why Statistics Matters for ML
Batch statistics and mini-batch noise
Moderate batch size. The batch statistics are somewhat stable (stability: 83%), giving reasonable gradient estimates. This is a common sweet spot for many models.