![]() ![]() The interesting things to note here are that = 79, regardless of the sample size, but the standard deviation decreases as n increases. Pay particular attention to the standard deviation. The image below represents all possible sample means for samples of size 1 (individuals), 2, 3, 4, and 5 (the population). The standard deviation, though, is very different. This is actually reasonable, though, because we know that the mean of a random variable is also its expected value, and it makes perfect sense that the value we should expect from the sample mean is the same as the population mean! Interestingly, the mean of the sample means of size 2 is 79" as well. There are 10 such samples ( 5C 2 = 10), shown below, along with their corresponding sample means. (Source: NBC Sports) The mean of the population is 79", with a standard deviation of 2.37"įirst, let's consider the different samples of size 2. To investigate these, let's look at a particular population.Ĭonsider the heights of the players from the starting line-up from the 2008 Men's Olympic Basketball gold medal game - Jason Kidd (76"), LeBron James (80"), Kobe Bryant (78"), Carmelo Anthony (78"), and Dwight Howard (83"). The big question, then, is the distribution of - in other words, what are its mean (the mean of the sample mean, ) and its standard deviation (the standard deviation of the sample mean, )? Isn't it's value determined by chance as well? Since we the individuals in a sample are randomly selected, the sample mean will depend on those individuals selected, so it, too, is a random variable. Let's look again at the definition of a random variable, from Section 6.1.Ī random variable is a numerical measure of the outcome of a probabilityĮxperiment whose value is determined by chance. Our goal in this section will be to characterize the distribution of the sample mean. ![]() The idea is this - unless we sample every single individual in the sample, there will be some error in our results. Sampling error is the error that results from using a sample to estimate information regarding a population. (Source: Gallup)Īll three of these are estimates based on samples In fact, they're probably not correct, due to sampling error. Voters are asked who they would vote for if the election were held today, (Source: Chicagoīarack Obama leads John McCain, 49% to 44%, when registered Highlights: 25.3 - In minutes, the average commute to work in 2007,Īn increase from 25.0 minutes in 2006. Social, economic and housing characteristics for the nation. The Census Bureau on Tuesday released the 2007 AmericanĬommunity Survey, the government's annual estimates of The average price of unleaded regular fell by 1.6 cents to $3.667Ī gallon on Saturday, from $3.683 a gallon, according to survey ![]()
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