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• The Midrange


  Rough estimate of the middle
• The Median

  Halfway point in a data set
• The Weighted Mean


  This is the mean of a data set in which not all values are equally represented
• Deciles

  Divide the distribution into 10 groups
• Standard Scores


  Tells how many standard deviations a data value is above or below the mean for a specific distribution of values
• Percentiles

  A position measure used in educational and health-related field to indicate the position of an individual in a group; divides the data set into 100 equal groups
• Reasons for Outliers

  • Measurement or observational error
  • Recording or clerical error
  • Subject not in the defined population
  • Value that occurred by chance
• Quartiles


  Divide the distribution into 4 groups
• Measures of Variation

  1. Range

  2. Variance

  3. Standard Deviation

  4. Coefficient of Variation
• Interquartile Range (IQR)


  Can be used as a rough measurement of variability in exploratory data analysis
• The Mode

  The value that occurs most often in the data set
• Remedies for Outliers


  • If outlier occurred as a result of an error: Attempt should be made to correct the error or value should be omitted entirely
  • If outlier occurred as a result of chance: Statistician or data analyst must make a decision whether to include outlier in the data interpretation or not
• Measures of Central Tendency


  1. Mean

  2. Median

  3. Mode

  4. Midrange
• Types of graphs

  • Bar Graphs
  • Pareto charts
  • Time series graph
  • Pie graph
• Exploratory Data Analysis

  Summary Statistics: Resistant statistics (Median & interquartile), Nonresistant statistics (Mean & standard deviation), Stem and Leaf Plots, Boxplots
• Types of frequency distributions

  • Categorical: Used for data that can be placed in specific categories such as nominal or ordinal-level data
  • Grouped: Used when the range of the data is large, data grouped into classes that are more than one unit in width
• Elements of a frequency distribution

  • Raw data
  • Data in original form
  • Class (quantitative or qualitative)
  • Where each raw data is placed
  • Frequency
  • Frequency distribution
• Importance of Boxplot: Can be used to graphically represent the data set, involves 5 specific values (minimum, Q1, median, Q3, maximum)
• Guidelines for class limits and boundaries

  1. Class limits should have the same decimal place value as the data

  2. Class boundaries should have one additional decimal place value (by + or -) and always end in a 5

  3. Start with the smallest number and end with the largest number

  4. Class width is obtained by subtracting the lower (or upper) class limit of one class from the lower (or upper) class limit of the next class
• Frequency distribution


  A listing or function showing all the possible values (or intervals) of the data
• Significance of a frequency distribution: To organize the data in a meaningful, intelligible way, enable the reader to determine the nature or shape of the distribution, facilitate computational procedures for measures of average and spread, enable the researcher to draw charts and graphs for the presentation of data
• Application in the lab: Histograms, Frequency Polygons, and Ogives


  Examples of different types of graphs and their applications
• Frequency is the number of occurrences of a repeating event per unit of time
• Organizing & Presenting Data

  1. Organize data using a frequency distribution

  2. Represent data in frequency distributions graphically using histograms, frequency polygons, and ogives

  3. Represent data using bar graphs, Pareto charts, time series graphs, and pie graphs

  4. Use the techniques of exploratory data analysis, such as the stem and leaf plots

  5. Draw and interpret boxplots and five-number summaries to discover various aspects of data