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lesson2 - Descriptive statistics

# lesson2 - Descriptive statistics - Lesson2 KafuWong2007...

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Ka-fu Wong  ©  2007 ECON1003: Analysis of Economic Data Lesson2-1 Lesson 2: Descriptive Statistics

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Ka-fu Wong  ©  2007 ECON1003: Analysis of Economic Data Lesson2-2 2004 Regional Nominal GDP per Capita Summary Statistics (yuan per person) Mean 14079.39 Standard Error 1912.88 Median 9608.00 Mode #N/A Standard Deviation 10650.44 Sample Variance 113431828.11 Kurtosis 7.14 Skewness 2.50 Range 51092.00 Minimum 4215.00 Maximum 55307.00 Sum 436461.00 Count 31 Guizhou Shanghai
Ka-fu Wong  ©  2007 ECON1003: Analysis of Economic Data Lesson2-3 Outline Measures of Central Tendency Measures of Variability Measures for two variables

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Ka-fu Wong  ©  2007 ECON1003: Analysis of Economic Data Lesson2-4 Population Parameters and Sample  Statistics population parameter  is number calculated from all the  population measurements that describes some aspect of  the population. The  population mean , denoted  μ , is a population  parameter and is the average of the population  measurements. point estimate  is a one-number estimate of the value of   a population parameter. sample statistic  is number calculated using sample  measurements that describes some aspect of the sample.
Ka-fu Wong  ©  2007 ECON1003: Analysis of Economic Data Lesson2-5 Measures of Central Tendency Central Tendency Mean Median Mode n x x n 1 i i = = Overview Midpoint of ranked values Most frequently observed value Arithmetic average

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Ka-fu Wong  ©  2007 ECON1003: Analysis of Economic Data Lesson2-6 The Mean Imagine an economy with N  individuals (that is, a  population )   with income X 1 , X 2 , …, X N Income per capita ( μ 29 Population Mean N X N 1 = i i = μ Sample x 1 , x 2 , …, x n Sample Mean n x x n 1 = i i = x
Ka-fu Wong  ©  2007 ECON1003: Analysis of Economic Data Lesson2-7 Arithmetic Mean The arithmetic mean (mean) is the most common measure of  central tendency For a population of N values: For a sample of size n: Sample size n x ... x x n x x n 2 1 n 1 i i + + + = = = Observed values N x ... x x N x μ N 2 1 N 1 i i + + + = = = Population size Population values

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Ka-fu Wong  ©  2007 ECON1003: Analysis of Economic Data Lesson2-8 Effect of extreme value on Arithmetic Mean The most common measure of central tendency Mean = sum of values divided by the number of values Affected by extreme values (outliers) 0 1 2 3 4 5 6 7 8 9 10 Mean = 3 0 1 2 3 4 5 6 7 8 9 10 Mean = 4 3 5 15 5 5 4 3 2 1 = = + + + + 4 5 20 5 10 4 3 2 1 = = + + + +
Ka-fu Wong  ©  2007 ECON1003: Analysis of Economic Data Lesson2-9 Median In an ordered list, the median is the “middle” number (50% above,  50% below)     Not affected by extreme values 0 1 2 3 4 5 6 7 8 9 10 Median = 3 0 1 2 3 4 5 6 7 8 9 10 Median = 3

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Ka-fu Wong  ©  2007 ECON1003: Analysis of Economic Data Lesson2-10 Finding the Median The location of the median: If the number of values is odd, the median is the middle  number.
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lesson2 - Descriptive statistics - Lesson2 KafuWong2007...

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