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# Data Analysis and Visua MATLAB CS 1173

UTSA

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This 1 page Class Notes was uploaded by Mireya Heidenreich on Thursday October 29, 2015. The Class Notes belongs to CS 1173 at University of Texas at San Antonio taught by Staff in Fall. Since its upload, it has received 40 views. For similar materials see /class/231394/cs-1173-university-of-texas-at-san-antonio in ComputerScienence at University of Texas at San Antonio.

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Date Created: 10/29/15

CS 1173 Populations and samples 110208 Most scientific experiments involve taking measurements of a relatively small number of items and then trying to deduce information about the entire population The small collection of items is called a sample The entire collection of all of the items of this type is called the population When thinking about scientific experiments it is important to keep these two ideas straight The population is usually huge The population mean and standard deviation are often denoted by the symbols u and 0 respectively These values are usually unknown since we can39t measure them directly On the other hand we can take a sample which is a collection of observations of the population For example in the Fisher iris data set we had 50 observations of each species The 50 observations form a sample for that species We can make statistical calculations using the sample and then infer what the true values for the population are This process is called making an estimation The most important thing we will want to estimate is the population mean The most common way to estimate the population mean is to just use the sample mean Suppose x x1x2 x3 xn represents a general set of n measurements We will use x to represent the sample mean and s to represent the sample standard deviation Similarly we will use u to represent the true population mean and o to represent the true population standard deviation 1 Estimating the population mean we just use the sample mean x to estimate the population mean u On charts with errorbars the center point usually represents x the sample mean 2 Estimating the population standard deviation we might just use the sample standard deviation s to estimate 0 but it turns out that a related value called the unbiased estimator is better Sometimes you will see the unbiased estimator denoted by 6 Example 1 IfY is a 20 x 4 array the MATLAB statement stdY is a row vector with 4 elements Each element is the unbiased estimator of the population based on that column 6 Example 2 If you wanted the actual sample standard deviation Y you would use stdY1 3 How much of a mistake are we likely to make in using the sample mean to estimate the population mean W In other words we take the sample estimate of the population standard deviation and divide it by the square root of n Average error standard error of the mean is SEM The 95 confidence interval for the population mean estimation is x 196SEMx196SEM In other words we are 95 certain that the true mean of the population is in the above interval

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