ch3 - Ch 3 NumericalDescriptive Techniques

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1 Ch 3 Numerical Descriptive  Techniques Recall that descriptive statistics consists of  graphical  summaries  and  numerical techniques . The most important numerical descriptive statistics that we will  study are: 1. Measures of Central Location Mean , Median, Mode 2. Measures of Dispersion or Spread – Range,  Standard Deviation , Variance, Coefficient of Variation 3. Measures of Relative Standing – Percentiles, Quartiles
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2 Measure of Central Location There are 3 common measures of central location: • The  Arithmetic   Mean  (average) is calculated by  summing the values and dividing by the number of  values. • The  Median  is  midpoint  of the values after they have  been ordered from the smallest to the largest. • The  Mode  is another measure of location and  represents the value of the observation that appears  most frequently . n X X X n X X n n i i + + + = = = 2 1 1
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3 The  average  (arithmetic mean) is  unique ; It is the only  measure of location where the  sum of the deviations  of  each value from the mean is zero. The histogram balances when supported at the arithmetic  average . List 1,2,2,3 0% 50% 0 1 3 4 5 6 7 8 List 1,2,2,5 0% 50% 0 1 2 3 4 5 6 7 8 List 1,2,2,7 0% 50% 0 1 2 4 5 6 7 8
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4 Why use median ?  It is not affected by extremely large or  small values and is therefore a valuable measure of location  when such values occur. What about the mode ?  This can be interpreted as the  “Fashion Mode” – it is the highest parts (peaks) of a histogram. What is the relationship between the mean, the median and  the mode?   For  symmetric  histograms,  mean = median = mode… But not all histograms are symmetric. If a histogram is  asymmetrical , say skewed to the left or to the right, the three  measures may differ. Here, what is important to realize is that  extreme values affect the average most; then the median; then  the mode. That is, the arithmetic mean is most sensitive to  extremely large or small values.
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5 Skewness  and the measures of centrality
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This note was uploaded on 03/14/2010 for the course ECON Statistics taught by Professor Yy during the Spring '10 term at Seoul National.

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ch3 - Ch 3 NumericalDescriptive Techniques

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