Statistics

There are two groups, A and B, of students in German language class. Each group consists of $15$ students. In the tables, down each column, a student’s ID and grade from the mid-year’s grade report are listed. The students are evaluated according to the grading scale from $1$ to $5$, while $1$ is the best grade and $5$ is the worst one. Calculate the coefficient of variation of grades for each group and determine in which group the grades are more balanced. I.e. choose the name of the group with more balanced grades and with the correct coefficient of variation ($\mathrm{\%}$) of grades. The value of the coefficient of variation is rounded to two decimal places. $$\begin{array}{|ccccccccc|}\hline \mathbf{\text{A -- students}}& 1& 2& 3& 4& 5& 6& 7& 8\\ \mathbf{\text{Grade}}& 2& 2& 2& 2& 3& 2& 1& 2\\ \\ \mathbf{\text{A -- students}}& 9& 10& 11& 12& 13& 14& 15& \\ \mathbf{\text{Grade}}& 2& 1& 3& 1& 3& 2& 3& \\ \hline\end{array}$$ $$\begin{array}{|ccccccccc|}\hline \mathbf{\text{B -- students}}& 1& 2& 3& 4& 5& 6& 7& 8\\ \mathbf{\text{Grade}}& 2& 1& 1& 2& 2& 3& 1& 2\\ \\ \mathbf{\text{B -- students}}& 9& 10& 11& 12& 13& 14& 15& \\ \mathbf{\text{Grade}}& 2& 1& 2& 1& 1& 1& 1& \\ \hline\end{array}$$

In the tables below the absent hours in lessons of $16$ boys and $14$ girls from one class for half of a year are listed. Use the variance of the number of absent hours to find out the students of which gender had the absence more balanced. I.e. choose the group with more balanced absence and the correct variance of the number of absent hours. The variance is rounded to two decimal places. $$\begin{array}{|cccccccc|}\hline \text{Girl's ID}& 1& 2& 3& 4& 5& 6& 7\\ \text{Absent hours}& 27& 61& 38& 61& 17& 39& 61\\ \\ \text{Girl's ID}& 8& 9& 10& 11& 12& 13& 14\\ \text{Absent hours}& 25& 21& 52& 16& 34& 9& 25\\ \hline\end{array}$$ $$\begin{array}{|ccccccccc|}\hline \text{Boy's ID}& 1& 2& 3& 4& 5& 6& 7& 8\\ \text{Absent hours}& 67& 56& 26& 36& 27& 55& 17& 34\\ \\ \text{Boy's ID}& 9& 10& 11& 12& 13& 14& 15& 16\\ \text{Absent hours}& 54& 46& 13& 48& 21& 49& 18& 14\\ \hline\end{array}$$

The students are evaluated according to the grading scale from $1$ to $5$, while $1$ is the best grade and $5$ is the worst one. In the pictures, there are visualizations of relative frequencies of grades in Math, which students of two groups (A and B) had in their year-class-reports. Calculate the variance of grades for each group of students and determine, in which group student performances of Math knowledge are more balanced. I.e. from the offered choices choose the group, which has more balanced grades and with the correct variance of grades. The variance is rounded to two decimal places.

A student performed repeated measurements of a length (in meters) and evaluated the main statistical characteristics: mean, standard deviation, variance and the coefficient of variation. Which of these characteristics has it's unit square meter?