Frequency Tables and Histograms

A WebQuest for Math 153 (Introduction to Statistical Methods )

Designed by

Donna Hiestand-Tupper
dtupper@ccbcmd.edu

 histogram

Introduction | Task | Process | Evaluation | Conclusion | Back to Lecture



Introduction

If you are reading an article in a  magazine or in the newspaper and come across a lot of numerical data, what would you do?  Let's be honest.  Most people would skip over the numbers and go right on reading the article.  However, if you were to come across a picture of the data, in other words, a graph, you might look at the graph and attempt to draw some conclusions, before you continued reading the article.

In this chapter, we looked at creating a various types of graphs, specifically histograms, bar graphs, pareto charts, pie graphs, scatter plots and box plots.  In this webquest, you will be creating a histogram to show how many runs are scored by your favorite baseball team. 


The Task

Go to the website http://mlb.mlb.com/NASApp/mlb/index.jsp. Go to the bottom of the page and click on the arrow next to "Jump To" and select the "roster" of your favorite team.

From the homepage of your favorite team.

 


The Process

 

  1. What is the name of the team you chose?
  2. Record the number of runs scored by each BATTER of your team.  The number of runs is located in the column labeled R.  Do NOT use the number of runs scored by a pitcher.  These are the runs give up by your favorite team.

    Runs                                                                                                
                                                                                     

     

  3. Use the SORT feature of your TI to sort the data.  It will make creating the frequency table easier.
  4. Use the formula class width = (largest data element - smallest data element) / (number of classes) to determine the class width.  You may round this number up to the next convenient whole number.  However, remember not to round up too much or you will have empty classes.  My advice is to use 7 classes.
  5. Beginning with the smallest data element, create your lower class limits;
  6. Create the corresponding upper class limits;
  7. Determine the tallies for each class;
  8. Create the frequency table
      Lower Class Limit    Upper Class Limit       Tally    
         
         
         
         
         
         
         


  9. Use Statdisk to create the corresponding histogram; The printout from Statdisk must be submitted as part of the assignment.
  10. Compare to the histogram created by your TI. Use the ZoomStat feature of the TI to get a more accurate picture.
  11. Briefly describe the appearance of your histogram.  Is is skewed, bell-shaped?
  12. Looking at the data and the histogram, is there a relationship between the players who scored few runs and the number of at bats they had?  The number of  "at bats" can be found in the column labeled AB.
  13. Hand in the histogram that corresponds to the frequency table created above.   However, I also want you to create a histogram using a class width of 10 and a class width of 30.  Does the shape of the distribution change with the change in class width?

Evaluation

You are required to answer each of the above questions.  When grading your web assignment, I will be using the rubric below.  Each category (calculation, use of technology, theory and written responses) is worth 25 points.  The number of points you get per category is based on the ratings excellent, good, acceptable, poor or blank.   Use the rubric below as a self-check before turning in your assignment.

Excellent
1
(25 Points)
Good
2
(20 Points)
Adequate
3
(15 Points)
Poor
4
(10 Points)
Blank
5
(0 Points)
Score
 

Calculations

 

No calculation or roundoff errors are present.

Roundoff errors are present.

Calculation errors present.

Calculation and roundoff errors were made.

No Calculations Shown

                   
 

Use of Technology

 

 

Shows complete and appropriate use of Statdisk & TI.

Shows appropriate use of Statdisk & TI, but a calculation error is present.

Limited or inappropriate use of Statdisk or TI.

No use of Statdisk, but TI-83 was used.

No use of Technology evident.

       
 

Theory Comprehension

 

 

Shows complete comprehension of the Statistical Theory.

Understands most of the theory, however minor errors made.

Shows some understanding of the theory, however explanations are unclear.

Shows limited understanding of the theory.

No understanding of theory evident.

        
 

Written Responses

 

Well written.  Neat, typed. No grammatical or spelling errors.

Ideas clearly presented, but spelling or grammatical errors are present.

Poorly written response.  Many spelling or grammatical errors present.

Poorly written response.  Many spelling or grammatical errors present. Assignment is hand written.

Questions left blank.

          

Conclusion

Although technology will always give us a histogram of our data, the histogram may be misleading if the correct number of classes (or bin width) is not used.  Too many classes leads to a picture with too much information.  Not enough classes gives us an unclear picture.  The apparent shape of the distribution is affected by the number of classes chosen.  Convention tells us to use between 5 and 20 classes, depending on the number of data elements.  Rounding up the class width does make creating the frequency table easier, but rounding too much leads to empty classes at the end bars.   Rounding down leads to data elements not fitting into any classes.  Using pictures to represent data allows people to get a visual representation of data.   However, remember what Mark Twain said, "There are lies, damn lies, and statistics."


Last updated on January 22, 2005. Based on a template from The WebQuest Page