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Chapter 3 Notes

# Chapter 3 Notes - c Chapter 3 Descriptive Statistics...

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c. Chapter 3: Descriptive Statistics: Numerical Measures Objectives: 1. Calculate and describe the characteristics of the measures of center. 2. Calculate and describe the characteristics of the measures of dispersion. 3. Describe data in terms of center, dispersion, and skewness. 4. Convert data to standardized values. 5. Describe data occurrences using Empirical Rule. 6. Be able to identify outlier. A. Introduction – We have looked at graphical representations and basic numeric descriptors (i.e.: minimum, maximum, range, mode) for numeric data. In this chapter, we will elaborate on more sophisticated ways of summarizing data using numeric indices.

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These numeric indices describe three major properties of numeric data : 1. Location (Center) 2. Dispersion (Variation or Spread) 3. Shape B. Measures of Location (Section 3.1) 1. Mean – average; value around which observations tend to cluster; balance point of histogram. a. Population mean ( μ ) μ = N X N i i = 1 b. Sample mean ( X ) X = n X n i i = 1 Example: Audit Data
c. The mean is susceptible to (influenced by) outliers. 2. Median – the point at which half the data lie above and half the lie below a. If the sample size is odd, the median is the middle value.

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