Thus, in above case X ̄ = 195 mg/ dl estimates the population mean μ = 200 mg/dl. However, the precision with which sample results determine population parameters needs to be addressed. This means, sample mean ( X ̄) estimates the true but unknown population mean (μ) and sample SD (s) estimates population SD (s). These sample results are used to make inferences based on the premise that what is true for a randomly selected sample will be true, more or less, for the population from which the sample is chosen. If one draws three different groups of 10 individuals each, one will obtain three different mean and SD. Cholesterol of the most of individuals is between 190-210mg/dl, with a mean (μ) 200mg/dl and SD (s) 10mg/dl.
S = sample SD X - individual value X ̄- sample mean n = sample size.įigure 1a shows cholesterol levels of population of 200 healthy individuals. Thus, a low SD signifies less variability while high SD indicates more spread out of data. If observations are more disperse, then there will be more variability. In other words, it characterizes typical distance of an observation from distribution center or middle value. Other parameter, SD tells us dispersion of individual observations about the mean. It is the center of distribution of observations (central tendency). Sample mean is average of these observations and denoted by X ̄. The findings of this sample are best described by two parameters mean and SD. These findings are further generalized to the larger, unobserved population using inferential statistics.įor example, in order to understand cholesterol levels of the population, cholesterol levels of study sample, drawn from same population are measured. To study the entire population is time and resource intensive and not always feasible therefore studies are often done on the sample and data is summarized using descriptive statistics.
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