CECmath.48


TITLE:  A STATISTICAL STUDY ON THE LETTERS OF THE
                       ALPHABET
          or How to Win on "The Wheel of Fortune"

AUTHOR:  Philip McGoldrick, L.E. Rader Center;
         Sand Springs, OK

OVERVIEW: Statistics and probability play an important
part in our lives and are particularly useful in
helping us make wise decisions. This exercise will help
the students see that  there are mathematical rules
that can effect even our use of the English language.

GRADES/SUBJECT:  Appropriate for Grades 7 though 12.
                 Mathematics and English language.

PURPOSE: This exercise re-enforces the value of
statistical research and provides an interesting view
of the way people write.

OBJECTIVE(s):  Students will be able to:
1.   Gather appropriate information for simple
     statistical analysis.
2.   Calculate the probability of picking any letter at
     random from a piece of English literature.
3.   Develop skills in calculating percentage
     probabilities, in addition and rounding of
     numbers, and (if desired) in using the calculator.
4.   Evaluate his own research by comparing his results
     with those of other students and by answering
     related questions on the two worksheets provided.

RESOURCES/MATERIALS NEEDED:
Each student should have:
    1. A book, magazine, or newspaper.
    2. Worksheet 1 and a pencil.
    3. A calculator.

ACTIVITIES AND PROCEDURES:
1.   This lesson can be introduced by either showing a
     5 to 10 minute video clip of the T.V. show "Wheel
     of Fortune," or by playing the game of Hangman
     with the class for 5 to 10 minutes.
2.   Ask the questions: "Are there some letters that we
     use more than other?" "Are there some that we
     hardly use at all?" "Do you think there may be
     some Mathematical rules that could improve our
     chances of winning at these word games?"
3.   Have students choose a book or magazine to
     research our use of letters. Choose a page and a
     place to begin at random and begin to tally the
     letters one at a time, filling out the table
     provided on the first worksheet. Caution: do not
     "jump around" the page.
4.   Add up the totals, which should come to a grand
     total of about 300 (more or less, if desired). Use
     a calculator to calculate (to 1 or 2 decimal
     places) the percentage probability of finding each
     letter. Check accuracy by adding up percents,
     which should total between 99% and 101% (allowing
     for rounding).
5.   The students now have enough information to answer
     and discuss the questions on the worksheets.

TYING IT ALL TOGETHER: Compare and discuss the students
results. Note the similarities and try to account for
the differences. Then use Worksheet 2 to review some of
the statistical consequences of the study done by the
students.
NOTE: Questions, such as 1, 3, 6, and 8 have no right
or wrong answer.


WORKSHEET 1

NAME _______________________         DATE __________

                  A STATISTICAL STUDY
            ON THE LETTERS OF THE ALPHABET
        or How to Win on "The Wheel of Fortune"

Name of the book or magazine being used for your
survey:  ______________________________ page:______


              Survey at least 300 letters
____________________________________________________
|        |                          |       |      |
| LETTER |            TALLY         | TOTAL |  %   |
|________|__________________________|_______|______|
|___A____|__________________________|_______|______|
|___B____|__________________________|_______|______|
|___C____|__________________________|_______|______|
|___D____|__________________________|_______|______|
|___E____|__________________________|_______|______|
|___F____|__________________________|_______|______|
|___G____|__________________________|_______|______|
|___H____|__________________________|_______|______|
|___I____|__________________________|_______|______|
|___J____|__________________________|_______|______|
|___K____|__________________________|_______|______|
|___L____|__________________________|_______|______|
|___M____|__________________________|_______|______|
|___N____|__________________________|_______|______|
|___O____|__________________________|_______|______|
|___P____|__________________________|_______|______|
|___Q____|__________________________|_______|______|
|___R____|__________________________|_______|______|
|___S____|__________________________|_______|______|
|___T____|__________________________|_______|______|
|___U____|__________________________|_______|______|
|___V____|__________________________|_______|______|
|___W____|__________________________|_______|______|
|___X____|__________________________|_______|______|
|___Y____|__________________________|_______|______|
|___Z____|__________________________|_______|______|
                                    |       |      |
                      GRAND TOTAL   |       | 100% |
                                    |_______|______|


HELP:   To find percents, use the calculator:
          _____    ___    ___________    ___
         |     |  |   |  |           |  |   |
         |TOTAL|  | / |  |GRAND TOTAL|  | % |
         |_____|  |___|  |___________|  |___|


                Complete the following:

TOP TEN LETTERS
1. _______      ______ %
2. _______      ______ %
3. _______      ______ %       BOTTOM FIVE LETTERS
4. _______      ______ %       22. ______   _____ %
5. _______      ______ %       23. ______   _____ %
6. _______      ______ %       24. ______   ______ %
7. _______      ______ %       25. ______   ______ %
8. _______      ______ %       26. ______   ______ %
9. _______      ______ %
10. ______      ______ %


                   SURVEY QUESTIONS

1.  How many vowels are in the TOP TEN? ___________ 2.
Which consonants would be the most useful in
    "Wheel of Fortune"?
    _____, _____, _____, _____, _____, _____
3.  Which vowel might be the least useful? ________
4.  What percentage of all the letters surveyed were
    vowels?  ________
5.  See if you can make ten different words using
    only the top five letters.
___________________________________________________
___________________________________________________


WORKSHEET 2

NAME _______________________         DATE __________


                LETTERS OF THE ALPHABET
               (Statistical Conclusions)

TRUE OR FALSE:

1.   You should never expect to find the letter Q on
     "The Wheel Of Fortune."
          T       F
2.   Almost every word requires a vowel.
          T       F
3.   The letter K is useful when playing the games of
     "Hangman" and "Wheel of Fortune."
          T       F
4.   I  and  O  are the most useful vowels.
          T       F
5.   The Top Ten letters account for about 75% of the
     letters needed to write in the English language.
          T       F
6.   The English language could get along fine without
     the letters J, Q, and X.
          T       F

BONUS: Explain any of your answers to questions 1
through 6.
_________________________________________________
_________________________________________________

7.   If you were producing stickers with letters of the
     alphabet for use in labeling personal items, such
     as books, pens, bags and bedroom doors, which of
     these letters would you need most?   (Circle 5
     answers)
          A     B     C     D     E
          F     G     H     I     J

8.   To do a more accurate study for the above
     "alphabet stickers," I would need to make a survey
     of...        (Circle the best answer)
          (a) a popular magazine
          (b) a list of students names
          (c) a dictionary
          (d) a novel

9.   In the game of "Scrabble," which of these letters
     would you expect to be worth the most points?
     Hint: the harder it is to use, the more points it
     is worth.  (Circle the best answer)
          H       V       S

10.  In "Scrabble," which of these letters would you
     expect to be worth only 1 point?
     (Circle the best answer)
          Q       N       K


                   SUGGESTED ANSWERS
                  (Answers may vary)

WORKSHEET  1:

1.  Four.
2.  R, S, T, L, N, plus one more.
3.  U.
4.  About 30% to 40%
5.  Answers will vary.


WORKSHEET 2:

1.  False.
2.  True.
3.  True or False. (K would be a good letter to use
    to make the game difficult.)
4.  False. (E is usually better.)
5.  True.
6.  True or False. (How would you replace them?)
7.  A, E, H, I, plus one other.
8.  Answers will vary. Answer (b) may be most useful
    since people like to label things with their
    name.
9.  V.
10.  N.