Getting Ready for AP STATISTICS: VOCABULARY BASICS

As you start the study of statistics, you will find topics and equations that you have studied in previous classes.  Mean-median-mode, for example, should quickly bring to mind average-middlemost-most frequent.  Other familiar terms have unique definitions for statistics class.  Meanings aren’t as much “different” as they are more “specific” and carry definite implications. 

What follows is not a complete list, but rather a sampling of the vocabulary with explicit meanings in the course.  There are only 10 here to get you started and a suggestion for continuing to prepare for AP Stats on your own.

Population: The complete set of data elements is termed the population.

Sample: A sample is a portion of a population selected for further analysis.

Parameter: A parameter is a characteristic of the whole population.

Statistic: A statistic is a characteristic of the sample.

                 Notice that the P’s are associated with each other and 
                 the S’s are associated with each other:  
                 Parameter is to Population as Statistic is to Sample

Individual refers to the elements in a set

Variable refers to the characteristics describing individual elements of a set.

Qualitative data are non-numeric or categorical data.

Quantitative data are numeric and can be either Discrete or Continuous.

     Discrete: numeric data that have a finite number of possible values.  When opinion surveys evaluate answers like “Strongly disagree, Disagree, Neither disagree or agree, Agree, Strongly agree, each possible answer is given a discrete numeric value so meaningful statistical computations can be made.  The same information could be gathered through options like “on a scale of 1 to 5...”

Data counts are always discrete: for example, the number of students enrolled in your statistics classes.

     Continuous: numeric data that have infinite possibilities: the set of all counting numbers or the set of all real, rational numbers between 1 and 2.



If you already have your textbook, look at the glossary to find other terms that you've run into before.  Read definitions to identify how these words might be similar and/or different from your past encounters with them. 

Getting Ready for AP STATISTICS: MEAN-MEDIAN-MODE

MEAN - MEDIAN - MODE

For those of us preparing to earn a 5 on the AP Statistics exam next spring, calculating mean - median - mode should be as natural as eating ice cream on a hot summer’s day.  The measures of central tendency were introduced in upper elementary math classes, but it isn’t until now that the various uses have important implications.  

CALCULATING MEASURES OF CENTRAL TENDENCY

MEAN is the same as “average”  or “arithmetic mean.”
     Add all of the elements and divide the sum by the number of elements.

MEDIAN is the middlemost.  Think of the middle of the street...that’s the median. 
One very easy way to find the median in a small group is to first put all numbers in ascending order. Then count from the right and left simultaneously until you get to the middle.

If there are an odd number of elements, there will be one in the middle that can’t be matched from both the right and left......the median.

If there are an even number of elements, the median is the AVERAGE of the two in the middle.

MODE is the most frequently appearing element.

USING CENTRAL TENDENCY TO DESCRIBE DATA

In Statistics, these measures are used to describe the “typical” element and the relative usefulness of each is determined by the level of measurement.  (Watch this site for an upcoming blog, "Getting Ready for AP Statistics: Levels of Measurement" and share examples with other followers.)

NOMINAL (entries are categories or qualitative data)......MODE

ORDINAL (qualitative or quantitative data)....................MEDIAN

INTERVAL (quantitative data)
--- Symmetric.............................................................MEAN
--- Skewed.................................................................MEDIAN


RATIO (quantitative data)
--- Symmetric.............................................................MEAN
--- Skewed.................................................................MEDIAN

A MEAN is useful only for interval or ratio data.  It considers all of the elements in the sample and is influenced by outliers.  The mean is pulled toward an extreme.

A MEDIAN is useful for all quantitative data: ordinal, interval, and ratio levels and is not effected by an extreme outlier.

A MODE is the only useful descriptor for nominal measurements.  It can be applied in all levels of measurement but may not exist or be meaningful in all cases.

 MEAN - MEDIAN - MODE ON A FREQUENCY GRAPH

  

 

USING A CALCULATOR FOR RECORDING MEAN - MEDIAN 

If you're using a TI-84 or similar grapher, check out the "LIST" and "STAT" buttons.  There are options for finding mean and median after listing the elements in a set.  While you're at it, find the owner's manual for the calculator you'll be using in class and look over the directions for inputting a list and calculating various statistical values.

Keep watching this site for more "Previews" of AP Stats, AP Calc, and other classroom courses.  Let's be prepared before school resumes!

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.