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 xx Sum of differences of each data point from the mean is ALWAYS = 0 1 () n i i = (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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QMM240 Descriptive Statistics - I Statistical Methods for Business I - Lecture Notes Page: 3 2) Median The 50th percentile half of the data points are less than or equal to the median and half are greater than or equal to the median Not as affected by extreme values as the mean Determining the median: The middle number when measurements are sorted Positioning point formula: 2 1 n Determines the sorted observation number of the median value. When n is even, take the average of the two values on either side of the positioning point.
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This note was uploaded on 04/01/2008 for the course QMM 240 taught by Professor Isken during the Winter '08 term at Oakland University.

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QMM240_W08_DescriptiveStats-I - QMM240 Descriptive...

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