2320L2.F19.pdf - Lecture 2 Numerical Descriptive Techniques...

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Cengage Learning 1 Lecture 2 Numerical Descriptive Techniques
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Cengage Learning 2 Numerical Descriptive Techniques Measures of Central Location Mean, Median, Mode Measures of Variability Range, Standard Deviation, Variance, Coefficient of Variation Measures of Relative Standing Percentiles, Quartiles Measures of Linear Relationship Covariance, Correlation
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Cengage Learning 3 Measures of Central Location The arithmetic mean , a.k.a. average or mean , is the most popular and useful measure of central location. Sum of the observations Number of observations Mean =
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Cengage Learning 4 Notation When referring to the number of observations in a population , we use uppercase letter: N When referring to the number of observations in a sample , we use lower case letter: n The arithmetic mean for a population is denoted with Greek letter “mu”: The arithmetic mean for a sample is denoted with an “x - bar”:
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Cengage Learning 5 Arithmetic Mean Population Mean Sample Mean
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Cengage Learning 6 The Arithmetic Mean is appropriate for describing measurement data, e.g. heights of people, marks of student papers, etc. is seriously affected by extreme values called “outliers”.
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Cengage Learning Measures of Central Location The median is calculated by placing all the observations in order; the observation that falls in the middle is the median. Data: {0, 7, 12, 5, 14, 8, 0, 9, 22} N=9 ( odd ) Sort them bottom to top, find the middle observation: 0 0 5 7 8 9 12 14 22 Data: {0, 7, 12, 5, 14, 8, 0, 9, 22, 33} N=10 ( even ) Sort them bottom to top, the middle is the simple average of observations 8 and 9: 0 0 5 7 8 9 12 14 22 33 median = (8+9)÷2 = 8.5 Sample and population medians are computed the same way. 7 3.7
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Cengage Learning 8 Measures of Central Location The mode of a set of observations is the value that occurs most frequently . A set of data may have one mode (or modal class), or two, or more modes. Mode is a useful for all data types, though mainly used for nominal data. For large data sets, the modal class is much more relevant than a single-value mode.
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