## Saturday, August 4, 2012

### 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.

## HISTOGRAM

Individual data points are collected into categories which are represented in adjacent bars.
Can compare to normal curve
Usually vertical axis is a frequency count of items in a category
More difficult to compare two data sets
Use only with continuous data

## BAR CHART

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

## 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.
continuous data sets
Interim data can be inferred
from graph line

## FREQUENCY POLYGON

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

## 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.
to see in
Shows exact
values and entire
sample set
Shows min, max,
and outliers
must be
continuous

## 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.
Easily identify min, max, gaps, clusters,
and outliers
Disadvantages:  Central tendencies difficult to visualize

## 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.

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

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.