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Data

Data. Handbook Chapter 4 & 5. Data. A series of readings that represents a natural population parameter It provides information about the population itself. Organizing Data. Important prelude to describing and interpreting data. Charting Data. Tables Organized by rows and columns.

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Data

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  1. Data Handbook Chapter 4 & 5

  2. Data • A series of readings that represents a natural population parameter • It provides information about the population itself

  3. Organizing Data • Important prelude to describing and interpreting data

  4. Charting Data • Tables • Organized by rows and columns Column 1 Column 2 Column 3 Row 1 Row 2 Row 3

  5. Charting Data • Graphs • Organized by horizontal (abscissa) and vertical (ordinate) axes

  6. Charting Data • Graphs • Proper legend • Properly labeled axes

  7. Graphs • Multiple graphs used for comparing data should map the same variables on the ordinate and abscissa and use the same scale for each graph.

  8. Describing data • Descriptions of data indirectly describes actual population parameters • Describing the data distribution is a first step in this process

  9. Data Distributions • Pattern of frequency • Frequency is how often a particular value or set of values occurs in a data set

  10. Histogram Frequency Graph

  11. Types of distributions • Uniform • Unimodal • Bimodal • Normal • Skewed

  12. Uniform • The distribution has an equal frequency (number of occurrences) of each value or category of values

  13. Uniform Distribution of Tree Heights

  14. Uniform Frequency Graph

  15. This is not a uniform distribution.

  16. Unimodal • The distribution has an unequal frequency (number of occurances) of each value or category of values • The distribution has distinct central values that have a greater frequency than the others

  17. Unimodal Distribution of Tree Heights

  18. Unimodal Frequency Graph

  19. Skewed • The distribution has distinct central values that have a greater frequency than the others • The less frequent values are not evenly distributed on either side of the high point

  20. Skewed Distribution of Tree Heights

  21. Skewed Frequency Graph

  22. Bimodal • The distribution has two distinct values or sets of values that have greater frequencies than the others • These values are separated from one another by less frequent values • Often indicative of two populations

  23. Bimodal Distribution of Tree Heights

  24. Bimodal Frequency Graph

  25. Two Populations of Trees

  26. Normal • Frequencies are equally spread out on either side of a central high point • Bell shaped • Most frequent type of distribution

  27. Normal Frequency Graph

  28. Interpreting Data • Descriptive statistics are used to summarize data • Several descriptive statistics are used to describe two important aspects of data distributions: • Central Tendency • Dispersion

  29. Central Tendency • Most data are spread out around a central high point • The central values are the ones that occur most often and thus important to report

  30. Measures of Central Tendency • Three common measurements • Mean • Average value • Median • Center value • Mode • Most frequent value

  31. Mean • “Typical Value” N Mean = S Xi i=1 N

  32. Normal Distribution and Central Measures • In a perfectly normal distribution the mean, median and mode are all the same

  33. Perfectly Normal Distribution

  34. Dispersion • The distribution of values that occur less often • The spread of the data around the central values is important to report • Dispersion is about the degree of clustering of the data

  35. Measures of Dispersion • Two common measurements • Range • Distance between the lowest and highest values • Standard Deviation • Average deviation from the mean

  36. Calculate Mean and Range

  37. Ranges

  38. Calculating Standard Deviation

  39. Normal Distribution and Dispersion • 68.26% of values fall within one standard deviation on either side of the mean • 95.44% of values fall within two standard deviations on either side of the mean • 99.74% of values fall within three standard deviations on either side of the mean

  40. Normal Distribution and Standard Deviation

  41. Graph of Dispersion

  42. Accuracy & Precision

  43. Accuracy

  44. Error • Error = Accuracy of a particular data point relative to an accepted value • Absolute Error = I Accepted – Data I • Percent Error = I Accepted – Data Ix 100 Accepted

  45. Precision • Precision is a measure of how consistent the data within a data set are relative to each other • One measure of precision of a data set is the standard deviation SD provided that m (the mean) is the accepted value • m+ SD

  46. Calculation of SD of a Data Set N 1/2 SD = S (m –Xi)2 i=1 N-1

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