1.1: Representing 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

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

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]”

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