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