STATS Module 2

• Organizing and Graphing Data


  • Explains how to organize and display data using tables and graphs
  • How to prepare frequency distribution tables for qualitative and quantitative data
  • How to construct bar graphs, pie charts, histograms, and polygons for such data
  • How to prepare stem-and-leaf displays
• Raw data


  Data recorded in the sequence in which they are collected and before they are processed or ranked
• Quantitative raw data


  • Ages (in years) of 50 students selected from a university
• Qualitative (or categorical) raw data


  • Status of 50 students (F, SO, J, SE)
• Ungrouped data


  A data set that contains information on each member of a sample or population individually
• Frequency distribution


  A list of all categories and the number of elements that belong to each of these categories
• Relative frequency


  Frequency of a category divided by the sum of all frequencies
• Percentage distribution


  Relative frequency multiplied by 100
• Graphical presentation of qualitative data

  • Bar graph
  • Pareto chart
  • Pie chart
• Bar graph


  A graph made of bars whose heights represent the frequencies of respective categories
• Pareto chart


  A bar graph with bars arranged by their heights in descending order
• Pie chart


  A circle divided into portions that represent the relative frequencies or percentages of a population or a sample belonging to different categories
• Frequency distribution for quantitative data lists all the classes and the number of values that belong to each class
• Class width


  The difference between the lower limits of two consecutive classes

  
• Class midpoint or mark


  The average of the lower and upper limits of a class
• Constructing frequency distribution table


  1. Determine number of classes

  2. Calculate approximate class width

  3. Decide on class width

  4. Determine lower limit of first class

  5. Construct frequency distribution table
• Histogram


  A graph in which classes are marked on the horizontal axis and the frequencies, relative frequencies, or percentages are marked on the vertical axis
• Frequency polygon


  A graph formed by joining the midpoints of the tops of successive bars in a histogram with straight lines
• Frequency distribution curve


  A smooth curve that results when the number of classes is increased and the width of classes is decreased for a very large data set
• Single-valued classes


  Classes where observations in a data set assume only a few distinct (integer) values
• Frequency distribution


  A tabular arrangement of data that shows the number of observations (frequency) in each class
• Relative frequency


  The frequency of a class divided by the total number of observations
• Percentage


  The relative frequency multiplied by 100
• Constructing a frequency distribution table


  1. Determine the minimum and maximum values

  2. Decide on the number and width of classes

  3. Count the number of observations in each class

  4. Calculate the relative frequency and percentage for each class
• Single-valued classes


  • Classes made of single values, not intervals, used for discrete data with few possible values
• Cumulative frequency distribution


  The total number of values that fall below the upper boundary of each class
• Cumulative relative frequency


  The cumulative frequency of a class divided by the total number of observations
• Cumulative percentage


  The cumulative relative frequency multiplied by 100
• Shapes of histograms


  • Symmetric
  • Skewed to the right
  • Skewed to the left
  • Uniform or rectangular
• Stem-and-leaf display


  A way to organize quantitative data by dividing each value into a stem (leading digits) and leaves (trailing digits)
• Creating a stem-and-leaf display

  1. Separate the data into stems and leaves

  2. Arrange the leaves for each stem separately
• Advantages of stem-and-leaf displays include not losing information on individual observations
• Grouped stem-and-leaf displays can be created by grouping the stems
• Split stem-and-leaf displays can be created by splitting the stems into two parts