1.1: Representing Data

**Bar graph**: used to display categorical dataBars must be separated from each other and even in width

**Pie chart**: used to display categorical data as a percentage of the wholeGenerally 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 dataEasier to see data in more detail when stem leaf plots are split

**Histogram**: essentially a bar graph for quantitative dataRelative 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 percentilesMade 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

**Bar graph**: used to display categorical dataBars must be separated from each other and even in width

**Pie chart**: used to display categorical data as a percentage of the wholeGenerally 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 dataEasier to see data in more detail when stem leaf plots are split

**Histogram**: essentially a bar graph for quantitative dataRelative 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 percentilesMade 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