Central Limit Theorem
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Tap a term to see what it means, or .
Calculate
Example: the waiting time at a bus stop follows an exponential distribution, which is quite skewed, with a mean of 10 minutes. The chart shows the means of 2,000 samples of 30 waits each. Change n to watch the bell form, or fall apart when n is small.
Step by step
What each term means
- Sample Mean (X̄ₙ)
- The mean of a sample of size 'n' drawn from the population. The theorem describes the distribution of these means.
- Is Distributed As (~)
- Means that, as the sample size 'n' grows, the distribution of sample means approaches a normal distribution.
- Normal Distribution (N)
- A continuous, bell-shaped probability distribution defined by its mean and variance.
- Population Mean (μ)
- The mean of the whole population. The distribution of sample means is centered on this value.
- Population Variance (σ²)
- A measure of how spread out the data are across the whole population.
- Sample Size (n)
- The number of observations in each sample. The variance of the distribution of sample means shrinks as 'n' grows.