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Transition to College: a statistics problem in conditional and proportional reasoning

Transition to College: a statistics problem in conditional and proportional reasoning


This activity encourages you to consider how responsible you are for your own learning and the impact that class attendance and the amount of study may have on college success. In this exercise, you will gain experience in interpreting data about conditional and proportional reasoning and you will explain conditional percentages using a contingency table.  Based on collected data, you will be able to calculate ratios, percentages, or odds of chance occurrence.

To prepare for this activity, you need to feel confident in your understanding of the concepts of fractions and proportions in mathematics.  Here's a short video from Jimmy Chang, a math teacher at St. Petersburg College, for you to review: Or you can review and test your knowledge in this short free tutorial, "Help with Proportions," from Discovery Education:

As a part of this activity focused on statistical inferential reasoning, you should also reflect on what college success skills work best for you.

A statistics inferential reasoning problem that relates to issues commonly found in the difficult transition from high school to college.

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Dr. William Griffith, award-winning professor of statistics, University of KentuckyThis exercise was developed by Dr. Bill Griffith, Department of Statistics at the University of Kentucky. A similar kind of activity has been used in his course, STA210 “Introduction to Statistical Reasoning,” which is a component of the University’s general education program (see more on this UK Core competency at  Successful students who complete this course at UK should be able to articulate how statistical science can be used to address uncertainty in many of our decisions and decide whether a statistical argument (that is used, for example, in the mainstream media) is valid.

First: A Reflection on Transition from High School to College

The transition from high school to college is a difficult one for many students. Many academic and non-academic issues arise. There is an extensive literature on this (listed at the end of this module) and much of that research is summarized in this interview on “College Transition” by Derek Melleby with Eric Bierker of The College Transition Group, Center for Parent/Youth Understanding.

Students in two freshman level courses at Wichita State University were asked to describe the transitional issues they faced in their first semester and to give advice to incoming students. What they had to say are pretty much the types of issues that most incoming college students face:

Top Ten Issues Identified by Freshmen in College
(in order of importance)

  1. Personal responsibility: In college you have freedom to do as you go where you do as you wish. … The student carries 98% of the responsibility and control.
  2. Class attendance: As a college student, you will decide whether you want to go to class or not. Being absent from class will hurt you in the long run.
  3. Teacher attitudes: Your instructors will not hound you to do your work.  … Get to know your teachers. If your teachers know you, it will be easier for them to help you if you're having trouble.
  4. Types of assignments: In high school you were probably given a homework assignment every day. Now you have a large task assigned to be done at a certain time. Once you get an assignment, start working on it right away. It takes a daily effort to keep up.
  5. Importance of performance: Don't take your courses or studies lightly. The decisions you make in college will decide your future, in some respects. Remember that you are here for an education.
  6. Time management: The amount of free time you have in college is much more than in high school. Always have a weekly study schedule to go by. Otherwise, time slips away and you will not be able to account for it. In college, you will have less in-class time, more outside of class work.
  7. Amount of study: In high school you might be a B student without studying. In college this means you will be a C/D student. To succeed, you have to study!
  8. Size of institution/classes: Lecture classes are much larger than high school classes. This can be scary for a new student.
  9. Difficulty of college work: College is probably going to be tougher than high school. Don't let that stop you!
  10. Social life: It might seem harder to make friends because of the size of a university. But there are a variety of organizations and activities. Get involved and meet people!


Source: "Top Ten Issues Identified by Freshmen in College" list adapted from “From High School to College – what to expect,” Duke University,

Second: Connect this to a statistics problem

Your success in college is a shared responsibility, but your share of this responsibility is now bigger than it was in high school. We will focus on two of the issues described above - - class attendance and amount of study.

First, study how a contingency table works: see the StatTrek Statistics and Probability Dictionary entry on conditional frequency.

Now, imagine a college class of 1,379 students in which there are about 30% new first-year students. See the student type counts below:





 New Freshman











In that class, each student was asked to answer a simple 2-question survey - see the survey questions below:


  1. Are you a first semester freshman? (Yes/No)
  2. Choose two (2) of the 10 issues listed as those problems most college students face when transitioning from high school.,  If you are a first semester freshman, please write which of these two issues that you think may give you more trouble. Maybe you do not think either issue will give you trouble, and in that case, answer which you think may give your fellow freshmen more trouble. If you are not a first semester freshman, you have experienced some college and you are to write which gave and/or gives you more trouble. If you find neither to be an issue, which one seems to give students that you know more trouble.

Third: Analyze Survey Results

All 1,379 students answered the survey with the following frequencies:

Transitions Survey Results Chart

Use your understanding of proportions to compute the answers to the following questions:

  1. If a student is selected at random in the class, what is the chance that s/he answered “amount of study” was an issue for him or her?
    HINT: How many total students are there? How many students answered "amount of study" is an issue?
  2. If a first semester freshman is selected at random, what is the chance that s/he answered  “amount of study”?
    HINT: How many first semester freshmen students are there?  Of those how many answered "amount of study" is an issue?
  3. If a student answered “amount of study,” what is the chance that s/he is not a first semester freshmen?
  4. What are some other questions you might have about this data? How would you solve that question?
  5. What differences did you uncover, if any, between what first semester freshmen anticipate and what those who are not first semester freshman have experienced in their transition to college? 


To get free help from an online study group, sign up at Open Study’s HippoCampus Statistics & Probability.for free.


Final Thoughts:

What about your own transition from high school to college? Reflect on which issues above most readily pertain to your own situation.

Here are some words of wisdom from Jerry O’Connor of New Mexico State University to first year college students:

Here are some movies on the transition to college:

Additional Resources:

On proportions and inferential reasoning

"Proportions," Brightstorm.

"Proportions and Proportional Reasoning," Wikibook.

On transition from high school to college

A good textbook (free online) explains what it means to be successful in college: College Success by Bruce Beiderwell et al., can be found at