One of the questions that students often ask after a difficult exam or at the end of the semester is, "Are you going to curve the grades?"  Generally, the students don't realize what they are asking.  They want to know whether or not their scores or grades will be adjusted (and generally they are expecting an upward adjustment).  In this assignment, we will see what it really means to grade on the curve.

The curve in question is the Bell curve which, under normal circumstances, would be the shape of the distribution histogram from a random sampling of student's scores for an exam or a course.  The peak of the curve is at the mean; that is the greatest number of students is expected to have the mean score.  The numbers then taper off in both directions from the mean to form a curve that looks like a bell.  Letter grades are then assigned based on either distribution percentages or standard deviations.  We will choose the standard deviation approach.  The standard deviation for a collection of scores is calculated using the following formula:

where n is the number of scores and x is one of the scores.  The first summation is the sum of the squares of each of the scores; the second summation is the sum of the scores and then that value is squared.  For example, if there are 3 scores, 68, 91, and 77, then the standard deviation is calculated as the square root of
 (3 * (68²+91²+77²) - (68+91+77)²) / (3 * 2)

Using the standard deviation approach works like this.  Anyone with a score that is within 1/2 standard deviation of the mean is assigned a grade of 'C'.  Anyone with a score that is greater than 1/2 standard deviation above the mean but less than or equal to 1 1/2 standard deviations above the mean is assigned a grade of 'B'.  Anyone with a score that is less than 1/2 standard deviation below the mean but greater than or equal to 1 1/2 standard deviations below the mean is assigned a grade of 'D'.  Anyone with a score greater than 1 1/2 standard deviations above the mean is assigned a grade of 'A'; and anyone with a score less than 1 1/2 standard deviations below the mean is assigned a grade of 'F'.

You are given two files, each with student names and a single score.  The file names are frst308.dat and frst317.dat   Both files use the following form to record a student's score

lastname,  firstname        score

There is a comma after the last name and the first name may be an actual name or for the students that have only one name (you will see what I mean in frst308.dat) the first name is replaced with a title or category.  All names are a single word - no two-part last names and no two-part first names.

You are to write a program which does the following:

1. Prompts for and reads in the name of the data file containing the names and scores and reads in the name of the report file to which your program will write most of its results.  You may choose the names for the report files.

 
2. Reads in the names and scores from the file.

 
3. Calculates the mean and standard deviation for the scores.  The standard deviation must be calculated using a function that you write named StdDev which calculates using the formula given above.  You are not allowed to use a standard deviation library function to calculate the standard deviation (even if you can find one); however, you may use the square root function from the cmath library.

 
4. Then, sort the students into alphabetical order (along with their scores).  This must be done with a function that you write named Sort.

 
5. Assign grades (A, B, C, D and F) to the students using the criteria specified above and write the names, scores, and grades to the report file.  This must be done using a function that you write named Assign.  Each line of the report file should have the form


firstname  lastname            score        grade

with one space between the first and last names and with the scores and grades in neat columns.
 

6. Finally, display on the screen the mean and standard deviation for the group.

When you have your program working, run it using frst308.dat as the data file and print the report file.  Also, capture the screen output by copying and pasting it into another file.  Then, run the program using frst317.dat as the data file and print the report file.  Capture the screen output by copying and pasting it into the same file as the first run.  Print the file with the two sets of screen output.

Print your source program and copy the .cpp file to the handin folder on the P drive, after giving it a name similar to your own.

Extra Credit Opportunities:

Extra credit will be given if the screen output shows the number of A's, B's, C's, D's, and F's assigned to the students, e.g. 3 A's, 10 B's, etc.  (fairly easy)
Extra credit will be given if the screen output shows the grade point average for the class.  A's are 4 points; B's are 3 points, C's are 2 points, D's are 1 point, and F's are 0 points.  (not bad)
Extra credit will be given if the screen output shows the median score.  The median is the middle score when the scores are sorted lowest to highest.  (harder)