QMM240_W08_DescriptiveStats-I

QMM240_W08_DescriptiveStats-I - QMM240 Descriptive...

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QMM240 Descriptive Statistics - I Statistical Methods for Business I - Lecture Notes Page: 1 Descriptive Statistics I Characteristic Interpretation Central tendency Data concentration? Typical or "middle values? Dispersion How variable? Unusual values? Shape Symmetric? Skewed? Flat? Peaked? Multimodal? Example: PERatios.xls I) Measures of Central Tendency: Can use dot plot, histogram and/or several statistics 1) Mean (or Average) The average of the sample n X X n i i 1 The mean of the population N X N i i x 1 Pro Con Familiar Sensitive to outliers Uses all the data
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QMM240 Descriptive Statistics - I Statistical Methods for Business I - Lecture Notes Page: 2 Obs # Value 1 0.2 2 0.1 3 4.8 4 2.7 5 25.6 Average 6.68 Notice how the mean falls between data point 5 and the rest of the data. No values are very "close" to the mean. Example: JDPowers.xls Use =Average( data range ) in Excel 1 87 93 98 ... 159 164 173 4639 125.38 37 37 n i i x x n Characteristics of the Mean 1 ( ) 0 n i i x x Sum of differences of each data point from the mean is ALWAYS = 0 1 ( ) n i i x x = (42 65) + (60 65) + (70 65) + (75 65) + (78 65) = (-23) + (-5) + (5) + (10) + (13) = -28 + 28 = 0 Mean is like a fulcrum. The data is balanced at the mean.
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