Glossary
Central Limit Theorem (CLT)
A fundamental theorem stating that the sampling distribution of the sample mean will approach a normal distribution as the sample size increases, regardless of the shape of the original population distribution.
Example:
Even if the distribution of individual incomes in a city is heavily skewed, the Central Limit Theorem ensures that the distribution of average incomes from large samples taken from that city will be approximately normal.
Sampling Distribution
The distribution of a statistic (like the mean or proportion) calculated from many different samples of the same size drawn from the same population.
Example:
If you repeatedly take samples of 30 students from your school and calculate the average GPA for each sample, the distribution of all those average GPAs would be the sampling distribution of the sample mean GPA.
Standard Deviation of the Sample Mean (σₓ̄)
A specific type of standard error that quantifies the variability of sample means around the population mean, calculated as the population standard deviation divided by the square root of the sample size.
Example:
If the population standard deviation of test scores is 10 points and you take samples of 25 students, the standard deviation of the sample mean would be 10/√25 = 2 points, indicating how much sample means typically vary.
Standard Error (SE)
The standard deviation of a sampling distribution, which measures the variability or typical distance of sample statistics from the true population parameter.
Example:
When analyzing the average height of students, the standard error tells you how much the average height from different samples is expected to vary around the true average height of all students.
Standard Error of the Sample Proportion (σₚ̂)
A specific type of standard error that quantifies the variability of sample proportions around the population proportion, calculated using the population proportion and sample size.
Example:
If 60% of students prefer online learning (p=0.6) and you survey samples of 100 students, the standard error of the sample proportion helps predict how much the proportion of online learners in your samples might vary from 0.6.