1.1: Representing Data

Methods of Displaying Data

Categorical Data

• Bar graph: used to display categorical data
  • Bars must be separated from each other and even in width
• Pie chart: used to display categorical data as a percentage of the whole
  • Generally not made by hand
  • In order to make a pie chart, one needs data for an entire group

Quantitative Data

• Dot plot: good for displaying quantitative data for a relatively small number of discrete values
• Stem plot: all but the final digit; good for displaying quantitative data
• Stem leaf plot: including the final digits; good for displaying quantitative data
  • Easier to see data in more detail when stem leaf plots are split
• Histogram: essentially a bar graph for quantitative data
  • Relative frequency histograms are made by taking the frequency in each class and dividing that by the total number of data points

Describing Univariate Data

“CUSS”: Center, Unusual, Shape, Spread

• Center: generally the point with half the data above and half below
  • Median
  • Put data in order
• Unusual: features that stand out about a given display of data
  • Eg. outliers, gaps
• Shape: notable physical features of the graph’s form
  • Eg. skewed left or right, roughly symmetric, or has some other noticeable physical feature
• Spread: how close to the center a range of data is to the center
  • Phrasing — “the spread is from [minimum value] to [maximum value], which is a range of [maximum value - minimum value]”

Relative Cumulative Frequency

• The Nth percentile of a distribution is the value such that N% of the observations fall at or below that value
• Relative cumulative frequency graph/ogive: a graph designed to answer questions involving percentiles
  • Made by extending the charts made for relative frequency histograms to include a column that keeps a cumulative total as we move through the classes
• To use a relative frequency graph, you will either—
  • Start on the x-axis at a given score, trace up to hit the graph, and then trace over to find the percentile
  • Start on the y-axis at a given percentile, trace over to hit the graph, and then trace down to find the corresponding score

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