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Chapter 4 Descriptive Statistics I. Numerical Description a. Intro i. Descriptive measures derived from a sample are statistics ii. Descriptive measures derived from a population are parameters b. Characteristics i. Central Tendency ii. Dispersion 1. How much variation is there in the data? 2. How spread out are the data values? 3. Are there unusual values? iii. Shape 1. Are the data values distributed symmetrically? 2. Skewed? 3. Sharply peaked? Flat? Bimodal? II. Central Tendency a. Mean i. Definition 1. Sum of the data values divided by number of data items ii. Characteristics 1. “Average” 2. Affected by every sample item

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3. The balancing point or fulcrum of a distribution if each item is physical weight 4. The distances from the mean to the data points always sum to 0 a. Regardless of shape b. Median i. Definition 1. The 50 th percentile or midpoint of the sorted sample data set ii. Characteristics 1. Especially useful when there are extreme values a. The mean is not affected by outliers c. Mode i. Definition 1. The most frequently occurring data value ii. Characteristics 1. A data set can have multiple or no modes at all 2. Easy to define, not easy to calculate – except for small data sets 3. Good for describing central tendency of categorical data 4. Not useful for continuous data because continuous data rarely repeats iii. Bimodal distribution or multimodal distribution occurs when dissimilar populations are combined into one sample
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## This note was uploaded on 04/18/2011 for the course BUS 370 taught by Professor Camp during the Winter '09 term at Indiana.

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