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\label{Statistics_Key}

The \textbf{Overall Problem Statistics} page displays the following 
data about the problems currently in the course:

\begin{description}

\item{\textbf{\#Stdnts}} Total number of students attempting the problem.

\item{\textbf{Tries}} Total number of attempts to solve the problem.

\item{\textbf{Max Tries}} Largest number of attempts to solve the problem by a student.

\item{\textbf{Mean Tries}} Average number of attempts.

\item{\textbf{S.D. tries}} Standard Deviation of the tries.

\item{\textbf{Skew Tries}} Skewness of the students tries.
\[ \frac{\sqrt{ \sum{(Xi - Mean)^3} / \#Stdnts}}{\sigma^3} \]

\item{\textbf{\#YES}} Number of students who solved the problem correctly.

\item{\textbf{\#yes}} Number of students who solved the problem by override.

\item{\textbf{\%Wrng}} Percentage of students who tried to solve the problem but were unable to.

\item{\textbf{DoDiff}} Degree of Difficulty of the problem.  

This statistics gives a measure of how many attempts it took the
students to get the problem correct.  Those students who did not get
the problem correct are not counted.  A value close to 0 indicates
most students who got the problem correct did so on the first attempt.
A value close to 1 indicates many attempts were required for students
to get the problem correct.  A negative value indicates students were
given points without attempting the problem.  A value of 'nan' means
there were no attempts made on the problem.

\[ 1 - \frac{\#YES+\#yes}{Tries} \]

\item{\textbf{DoDisc}} Degree of Discrimination of the problem.

The students are grouped based on their scores on the sequence which 
contains the homework problem.  The percent score of the bottom 25\% of
the students is subtracted from the percent score the to top 25\% of
the students.  This yields a number from -1 to 1. 1.0 indicates
all of the good students answered the problem correctly and none of the
poor students answered it correctly.  Conversely, a score of -1.0 indicates
all of the good students got the problem wrong and the bad students did
well.

\item{\textbf{weight}} The weight of the problem in the course (``points'').
The value shown is the weight of the problem for the individual computing the
statistics.  Individual student or section variations are not shown.

\end{description}

\textbf{Sequence Statistics}, that is compiled statistics on problems based on
their containing sequence, are also shown.  The following data are shown:

\begin{description}

\item{\textbf{\#Items}} The number of problem parts in the sequence.

\item{\textbf{Score Mean}, \textbf{Score STD}, \textbf{Score Max} \textbf{Score Min}}
The mean, standard deviation, maximum, and minimum of the scores of
the selected students on the given sequence.

\item{\textbf{Score N}}  The number of the selected students who submitted answers to problem parts in the sequence.

\item \textbf{Count Mean}, \textbf{Count STD}, \textbf{Count Max}, \textbf{Count Min} 
The mean, standard deviation, maximum, and minum count of correct
problem parts of the selected students on the given sequence.

\item \textbf{Count N} The number of the selected students who submitted answers to problem parts in the sequence.

\item \textbf{KR-21} The KR-21 reliability statistic measures the internal reliability of a test or exam.

To compute the KR-21 reliability statistic the following formula is used:

\[KR-21 = \frac{K}{K-1} \cdot \frac{1-(M \cdot (K-M))}{K \cdot s^{2}}\]

Where 
\begin{description}
\item{$K$} is the number of items in your test
\item{$M$} the mean score on the test
\item{$s$} the standard deviation of the scores on your test
\end{description}

\end{description}