how to measure a population
the difficulty in measuring a population lies in whatever you re attempting to analyze and what you re trying to accomplish data must be collected through surveys measurements observation or other methods gathering the data on a large population generally isn t done because of the costs time and resources required to obtain it all the doctors with patients who could use drug xyz in the u s likely weren t contacted to confirm this if you see an advertisement that claims 62 of doctors recommend xyz for their patients rather 62 of the doctors who responded to the several hundred or thousands of surveys that were sent out responded that they would recommend xyz this is a population sample population and investinga parameter is a characteristic of a population a statistic is a characteristic of a sample and samples can only result in inferences about a population characteristic inferential statistics allow you to make an educated guess about a population parameter based on a statistic computed from a sample randomly drawn from that population 2statistics such as averages or means and standard deviations are referred to as population parameters when they re taken from populations many such as a population s mean and standard deviation are represented by greek letters like mu and sigma these statistics are inferential in nature much of the time because samples are used rather than populations you don t have to use statistical inference if you have all the data for the population being studied because you won t have to use a sample of the population market and investment analysts use statistics to analyze investment data and make inferences about the market a specific investment or an index financial analysts can evaluate an entire population in some cases because price data has been recorded for decades the price of every publicly traded stock could be analyzed for a total market evaluation because the prices are recorded this is a population in terms of investment analysis an analyst can calculate parameters with all this data but the parameters used by analysts are only occasionally used in the same way that statisticians and scientists use them some of the parameters you might see used by investment analysts statisticians and scientists and their differences are alpha the excess returns of an asset compared to a benchmarkstandard deviation average amount of variability in prices used to measure volatility and riskmoving average used to smooth out short term price fluctuations to indicate trendsbeta measures the performance of an investment portfolio against the market as a wholealpha the probability of making a type i error or rejecting the null hypothesis when it is truestandard deviation average amount of variability in datamoving average smooths out short term fluctuations in data valuesbeta the probability of making a type ii error or incorrectly failing to reject the null hypothesis