In my statistics classes, I learned to use the variance or the standard deviation to measure the variability or dispersion of a data set. However, consider the following 2 hypothetical cases: the standard deviation for the incomes of households in Canada is $2,000 the standard deviation for the incomes of the 5 major banks in Canada […]
The central limit theorem (CLT) is often stated in terms of the sample mean of independent and identically distributed random variables. An often unnoticed or forgotten aspect of the CLT is its applicability to the sample sum of those variables, too. Since , the sample size, is just a constant, it can be multiplied to to obtain […]
According to the central limit theorem, if random variables, , are independent and identically distributed, is sufficiently large, then the distribution of their sample mean, , is approximately normal, and this approximation is better as increases. One of the most remarkable aspects of the central limit theorem (CLT) is its validity for any parent distribution of […]
Having taught and tutored introductory statistics numerous times, I often hear students misinterpret the Central Limit Theorem by saying that, as the sample size gets bigger, the distribution of the data approaches a normal distribution. This is not true. If your data come from a non-normal distribution, their distribution stays the same regardless of the […]
Introduction This is a follow-up post to my recent introduction of histograms. Previously, I presented the conceptual foundations of histograms and used a histogram to approximate the distribution of the “Ozone” data from the built-in data set “airquality” in R. Today, I will examine this distribution in more detail by overlaying the histogram with parametric […]
