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    1: \label{Statistics_Key}
    2: 
    3: The \textbf{Overall Problem Statistics} page displays the following 
    4: data about the problems currently in the course:
    5: 
    6: \begin{description}
    7: 
    8: \item{\textbf{\#Stdnts}} Total number of students attempting the problem.
    9: 
   10: \item{\textbf{Tries}} Total number of attempts to solve the problem.
   11: 
   12: \item{\textbf{Max Tries}} Largest number of attempts to solve the problem by a student.
   13: 
   14: \item{\textbf{Mean Tries}} Average number of attempts.
   15: 
   16: \item{\textbf{S.D. tries}} Standard Deviation of the tries.
   17: 
   18: \item{\textbf{Skew Tries}} Skewness of the students tries.
   19: \[ \frac{\sqrt{ \sum{(Xi - Mean)^3} / \#Stdnts}}{\sigma^3} \]
   20: 
   21: \item{\textbf{\#YES}} Number of students who solved the problem correctly.
   22: 
   23: \item{\textbf{\#yes}} Number of students who solved the problem by override.
   24: 
   25: \item{\textbf{\%Wrng}} Percentage of students who tried to solve the problem but were unable to.
   26: 
   27: \item{\textbf{DoDiff}} Degree of Difficulty of the problem.  
   28: 
   29: This statistics gives a measure of how many attempts it took the
   30: students to get the problem correct.  Those students who did not get
   31: the problem correct are not counted.  A value close to 0 indicates
   32: most students who got the problem correct did so on the first attempt.
   33: A value close to 1 indicates many attempts were required for students
   34: to get the problem correct.  A negative value indicates students were
   35: given points without attempting the problem.  A value of 'nan' means
   36: there were no attempts made on the problem.
   37: 
   38: \[ 1 - \frac{\#YES+\#yes}{Tries} \]
   39: 
   40: \item{\textbf{DoDisc}} Degree of Discrimination of the problem.
   41: 
   42: The students are grouped based on their scores on the sequence which 
   43: contains the homework problem.  The percent score of the bottom 25\% of
   44: the students is subtracted from the percent score the to top 25\% of
   45: the students.  This yields a number from -1 to 1. 1.0 indicates
   46: all of the good students answered the problem correctly and none of the
   47: poor students answered it correctly.  Conversely, a score of -1.0 indicates
   48: all of the good students got the problem wrong and the bad students did
   49: well.
   50: 
   51: \item{\textbf{weight}} The weight of the problem in the course (``points'').
   52: The value shown is the weight of the problem for the individual computing the
   53: statistics.  Individual student or section variations are not shown.
   54: 
   55: \end{description}
   56: 
   57: \textbf{Sequence Statistics}, that is compiled statistics on problems based on
   58: their containing sequence, are also shown.  The following data are shown:
   59: 
   60: \begin{description}
   61: 
   62: \item{\textbf{\#Items}} The number of problem parts in the sequence.
   63: 
   64: \item{\textbf{Score Mean}, \textbf{Score STD}, \textbf{Score Max} \textbf{Score Min}}
   65: The mean, standard deviation, maximum, and minimum of the scores of
   66: the selected students on the given sequence.
   67: 
   68: \item{\textbf{Score N}}  The number of the selected students who submitted answers to problem parts in the sequence.
   69: 
   70: \item \textbf{Count Mean}, \textbf{Count STD}, \textbf{Count Max}, \textbf{Count Min} 
   71: The mean, standard deviation, maximum, and minum count of correct
   72: problem parts of the selected students on the given sequence.
   73: 
   74: \item \textbf{Count N} The number of the selected students who submitted answers to problem parts in the sequence.
   75: 
   76: \item \textbf{KR-21} The KR-21 reliability statistic measures the internal reliability of a test or exam.
   77: 
   78: To compute the KR-21 reliability statistic the following formula is used:
   79: 
   80: \[KR-21 = \frac{K}{K-1} \cdot \frac{1-(M \cdot (K-M))}{K \cdot s^{2}}\]
   81: 
   82: Where 
   83: \begin{description}
   84: \item{$K$} is the number of items in your test
   85: \item{$M$} the mean score on the test
   86: \item{$s$} the standard deviation of the scores on your test
   87: \end{description}
   88: 
   89: \end{description}