Getting Ready for AP STATISTICS: COMMON GRAPHS

Statistics is the collection and analysis of data for the purpose of discovering trends, formulating conclusions, and making predictions.  Sometimes "picturing" the data can be useful in explaining relationships.  Several forms of visual display are taught in math classes that come before a formal Statistics class.  

Charts and graphs are used to display specific data, categories, trends, and other visualizations which may make it easier to understand statistical measurements.  The advantages and disadvantages of each display determine the best use for each.

EXAMPLE #1

 

HISTOGRAM 

Individual data points are collected into categories which are represented in adjacent bars.

Advantages:  Visually strong

                      Can compare to normal curve

                      Usually vertical axis is a frequency count of items in a category

Disadvantages:  Cannot read exact values because data is grouped into categories

                           More difficult to compare two data sets

                           Use only with continuous data

EXAMPLE #2

 

 

 

 

 

 

 

BAR CHART

Similar to Histogram but individual data points are represented in each bar, avoiding disadvantage of not being able to distinguish exact values.

EXAMPLE #3

LINE GRAPH

Plots continuous data as points and joins them with a line.  Multiple data sets can be graphed together with separate sets identified in a key.
Advantages:  Can compare multiple
                      continuous data sets
                      Interim data can be inferred
                      from graph line
Disadvantages:  Data must be continuous

EXAMPLE #4

 

FREQUENCY POLYGON 

Made by coloring in the area below a line graph.  From a histogram, construct the polygon by connecting midpoints of each column.
Advantages:  Attractive display
Disadvantages:  Ends may imply zero as
                           data points
                           Use only with continuous
                           data

 

 

EXAMPLE #5

SCATTER PLOT (DOT PLOT)

Displays the relationship between two factors of the experiment.  A line of best fit is used to indicate positive, negative, or lack of correlation.
Advantages:  Trends are easy
                      to see in
                      Shows exact
                      values and entire
                      sample set
                      Shows min, max,
                      and outliers
Disadvantages: Both data sets
                          must be
                          continuous

EXAMPLE #6

 

 

 

 

 

 

 

STEM AND LEAF DISPLAY

Data displayed in rows which can easily be converted to histograms or frequency graphs.  If rows become too long,  left column entries may be repeated.  Strings are most useful if entries are in numeric order.
Advantages:  Precise data list
                      Easily identify min, max, gaps, clusters,
                      and outliers
 Disadvantages:  Central tendencies difficult to visualize

EXAMPLE #7

BOX AND WHISKERS   (BOX PLOT)

Showing the five standard measures: median, upper and lower quartiles, smallest value, and largest value . Multiple boxplots can be drawn side by side to compare more than one data set. 

Advantages
    Shows 5-point summary and outliers
    Easily compares two or more data sets
    Handles extremely large data sets easily

Disadvantages
    Exact values are lost

EXAMPLE #8

Here's a graph that shows up frequently in calculus problems...

 OGIVE (CUMULATIVE LINE GRAPH)

Displays the total at any given time. The relative slopes from point to point will indicate greater or lesser increases; for example, a steeper slope means a greater increase than a more gradual slope.



For some of these visualizations, like the box and whiskers display or a line of best fit, it is necessary to calculate trends or measures of central tendency.  Can you find the mean? the median? the mode? the first quartile?  the standard deviation?

Definitions and calculations for these and other important principles in Stats will be covered in upcoming blogs.  A little review before school resumes can help get the new term off on the right foot.  Keep watching this sight for tips for AP Stats and other courses.