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Statistics AP

MATH 451/452

Statistics AP

  • Course ID:MATH 451/452
  • Semesters:2
  • Department:Mathematics
  • Course Rank:College Level
  • Teachers:Miguel Hernandez

Description and Objectives

The course AP Statistics is a one year course which serves to teach the student basic statistics at the university level while at the same time preparing him for the AP exam.  When successfully completed, this course should replace a one semester course in non-calculus based statistics (e.g. STAT 100 at University of Maryland, but not STAT 400).  The fact that we take a full year to do a semester course provides us with the opportunity to carefully explore certain concepts and prevents us from rushing through the material.

The topics for AP Statistics are divided into four major themes: exploratory analysis, planning a study, probability, and statistical inference. The time allocation for these blocks is as follows:  Approximately seven (7) weeks are spent on exploratory analysis, three (3) weeks are spent on study planning and data collection, seven (7) weeks on probability and ten (10) weeks on inferential statistics.

Calculators are essential to this course and are required for the AP Statistics exam.  Although there are many brands and models which are acceptable, I recommend the TI-84.  Much of what we do in demonstrations in class will be done on one of these machines. Please see me with any questions regarding this.  Minitab, a statistical program will be available on some of the machines in the computer lab for class projects.

Homework is given daily and comprises 20% of the overall grade. Quizes are given without warning but usually weekly and make-up 20% of the grade.  There are typically six (6) full-period exams per semester (three per quarter) and a two (2)-hour midyear and Final exam.  A final project on topics from the course will be assigned after the AP exam.  This will be in the form of a paper discussing study planning or an actual study with statistical results.  We are fortunate to live in a very “poll-centered” community (Washington D.C.) and will make use of this as the next Presidential and Congressional elections approach.

As we approach the May AP exam date, our classes will increasingly concentrate on review of the material for the exam.  We will have mini-mockAP exams daily in the final weeks before the actual exam.


Our textbook is Understandable Statisticsby Brase and Brase, ISBN 0395907683 and we will make additional use of the Baron’s Guide for AP Statistics.


Course Requirements


  • Exploratory analysis


Objective: Students should be able to detect important characteristics, such as shape, location, variability, and unusual values by examining data. From careful observations of patterns in data, students should be able to generate conjectures about relationships among variables. The notion of  variable is introduced with special attention to the notion of how variables relate permeates almost all of statistics. The difference between association and causation accompany this conceptual development so that our next topic of study planning is not tainted.

Students are taught to calculate by hand and by machine the statistical basics of: measures of central tendency (mean, median and mode) as well as measures of dispersion (variance, standard deviation and range).  For this segment all computations are “populational” as opposed to “sample”.  Next we look at graphical ways of displaying data such as histograms, barcharts, dot-frequency plots, box-and-whisker plots, stem-and-leaf plots and pie-graphs. Cummulative frequency plots are also discussed.


Text:  Chapter 1, 2 & 3 Brase & Brase



  • Study Design


Objective:  Students learn to devise a way to collect data such that unspoiled inferences may be made from said data.  Students learn that data must be collected according to a well-developed plan if valid information on a conjecture is to be obtained.  The plan must identify important variables related to the conjecture and specify how they are to be measured.  From the data collection plan, a model can be formulated from which inferences can be drawn.



Text: Baron’s Guide



  • Probability


Objective:  The student learns basic probability techniques.  Here they look at “games” and how to calculate the probability of “winning” such games. Combinatorics provide the basis for our “counting” skills. We look at conditional probability and use this as a spring board for discussing the idea of random samples already introduced in our segment on study planning.  The randomness of a normal distribution is discussed especially as it applies to the sampling on the randomness of the distribution of the samples themselves. Central limit theorem,Venn diagrams and descision theory are discussed but not stressed during this unit. Bayesian vs. non-Bayesian statistics round out the discussion.


Text:  Chapter 4 & 5 Brase & Brase

  • Statistical inference


In this segment, students will learn to select appropriate models to be able to make pronouncements or recommendations on dealing with certain data. Models and data interact in statistical work: models are used to draw conclusions from data, while the data are allowed to criticize and even falsify the model through inferential and diagnostic methods. Inference from data can be thought of as the process of selecting a reasonable model, including a statement in probability language of how confident one can be about the selection.  To be specific, we will learn about estimation of means, estimation of proportions, confidence intervals, tests, tests, -tests, differences of means and proportions.



Text:  Chapter 6, 7, 8, 9, 10 & 11


As we move toward the time of the AP exam, three students will be selected to give a presentation to the AP Biology students on the distribution. This cross curricular presentation of knowledge is an important part of learning one’s subject.  All students must prepare to be selected for this task.


Successful Students

Students may ask questions any time.  Office hours are plentiful and include before school every day, lunch hour every day and after school by appointment.  Students are encouraged to make use of the instructor’s email address:  or his extension on campus 301.365.0227×216


Summer Assignment

The only Summer assignment is to acquire a TI-84 Graphing calculator (can be the *Plus/Silver Edition/CE).