I've been given the question: $$\mbox{Given the dataset, with 15 observations}$$ $$\left(4,55;\; 6,51;\; 3,04; \; 5,60;\; 3,69;\; 5,12;\; 7,31;\; 7,80;\; 8,31;\; 3,83;\; 4,44;\; 6,47;\; 6,14;\; 8;76;\; 7,67 \right)$$ $\textbf{a)}$ Calculate the mean, standard deviation, coefficient of variation and quartiles. Build a $box-plot$.
$\textbf{b)}$ Interpret the results.
There is nothing in my notes showing the use of the semicolon ';' in the description of a dataset. I interpret this as such: $$\mbox{There are 4 occurences of 55 in class 1}$$ $$\mbox{There are 6 occurences of 51 in class 2}$$ $$\vdots$$ $$\mbox{There are 7 occurences of 67 in class 15}$$ Them with this interpretation, we have
$\textbf{a)}$ The median is $$\overline{x} = \sum \frac{4(55) + 6(51) + \cdots + 7(67)}{4+6+ \cdots + 7} \approx 48,756$$ The standard deviation will be $$s^2 = \frac{\sum (x_i - \overline{x})^2}{82} = \frac{(55 - 48,756)^2 + (51 - 48,756)^2 + \cdots + (67 - 48,756)^2}{82} \approx 110,031$$ The coefficient of variation will be $$CV(X) = \frac{s}{\overline{x}} = \frac{\sqrt{s^2}}{\bar{x}} \approx \frac{10,49}{48,756} \approx 0,215$$ The $box-plot$ can be drawn using $$Q_1 = \frac{n+1}{4} = \frac{82+1}{4} = 20,75$$ $$Q_2 = \frac{n+1}{2} = 41,5$$ $$Q_3 = \frac{3(n+1)}{4} = 62,25$$
$\textbf{b)}$ The results can be interpreted from $\overline{x}$, $s$ and the $box-plot$.
Is this interpretation of the semicolon in given the dataset correct?