EconSampStats Distr

# EconSampStats Distr - Introductory Statistics Stats 210...

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1 Introductory Statistics Stats 210 Sampling, Sample Statistics and the Sampling Distribution

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2 Sampling from a Population Now that we described the population thoroughly we are ready to take a sample from the population Note: We assume that we take a random sample from the population Random Sampling = Every possible sample of size N has the same probability of being selected
3 Sampling from a Population It is important to note that the observations in a sample (x 1 , x 2 , …, x N ) are random variables and have to be treated as such If all sample observations are drawn from the same population then every single observation has the same distribution as the population

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4 i.i.d. Random Sample Observations in an i.i.d random sample are independently and identically distributed This assumption consists of two parts Independent observations on X We need a random sample so every observation has the same probability of being picked Observations have the same distribution We sample from the same population Most data we will work with is i.i.d.
5 Describing the Sample We can use a variety of statistics to describe the sample Sample mean Sample variance Sample Correlation Sample Median Sample Interquartile Range Sample counterparts of what we learned so far

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6 The Sample Mean The Sample Mean is calculated by summing all sample observations and dividing by the sample size N The Sample mean is denoted by N x x x x X N + + + + = ...... 3 2 1 = = N i i x N X 1 1 X
7 The Sample Mean We will use the sample mean as an estimate of the population mean Therefore it is valuable to see them side to side N N N N x x x X 1 1 2 1 1 ...... + + + = ) ( ...... ) ( ) ( 2 2 1 1 K K X x p x x p x x p x + + + = μ

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8 The Sample Mean Two differences Sample mean uses a subset of observations from the population Sample mean weights every observation equally N N N N x x x X 1 1 2 1 1 ...... + + + = ) ( ...... ) ( ) ( 2 2 1 1 K K X x p x x p x x p x + + + = μ
9 Exsample Mean Assume you take a random sample of 8 observations from the population Sample: 10, 12, 16 ,20, 25, 30, 50, 45 Let’s calculate the sample mean 26 8 208 = = X

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10 Sample Median The sample median is the number such that half of all observations lie above and half lie below If N is even the sample median is the average of the two observations in the middle If N is odd the sample median is the (n+1)/2 (middle) observation
11 ExSample Median Assume you take a random sample of 8 observations from the population Arrange observation in order from lowest to highest Sample: 10, 12, 16 ,20, 25, 30, 45, 50 Let’s calculate the sample median 5 . 22 2 25 20 = + = M

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12 ExSample Median Assume you take a random sample of 7 observations from the population Arrange observation in order from lowest to highest Sample: 10, 12, 16 ,20, 25, 30, 46 Let’s calculate the sample median 20 = M
13 Mean vs. Median Note: Mean = Median if distribution is symmetric What are outliers?

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## This note was uploaded on 09/25/2010 for the course ECON 210 taught by Professor Pavan during the Winter '09 term at Northwestern.

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EconSampStats Distr - Introductory Statistics Stats 210...

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