Students encounter data and statistics in various occasions in their daily lives, be it in the news, in advertisements or later at work or at the university. It is therefore a widely accepted fact, that it is important for students to acquire the competencies on the one hand to interpret statistics and make reasonable judgements based on them, on the other hand use statistics to back up their arguments. Numerous representations of data can be used to that. Multiple representations provide a good possibility to make the connection between representations clear to students and shed light to their different focuses and intentions, which is why it is advisable to use them when dealing with data and statistics in class.

The main benefit of using ICT in data and statistics is that it is much easier to create sophisticated representations of data that was either manually typed in or even automatically captured by the software from a mathematical or physical model. ICT also enables teachers and students to easily vary parameters and dynamically view the changes the variation induces in the results. TT link

Absolute and relative frequency
For an event i, the absolute frequency n_i is the number of times the event occured in a statistical experiment.
The relative frequency is defined as the absolute frequency divided by the total number of events N in the experiment:

Pictogram and bar chart
One possibility of a graph is a pictogram. A pictogram uses symbols/icons to represent data.

Basic key figures
For a given sequence of events \left\{ x_1, x_2, ..., x_n \right\} some of the most basic, yet important, key figures in descriptive statistics are:

• Arithmetic means
  Defined as the quotient of the sum of all values divided by the number of values: \overline{x} = \frac{1}{n} \sum_{i=1}^n x_i
• Range
  Defined as the difference between minimum and maximum in the sample set.
• Median value
  Defined as the numerical value, which divides the sample set in two equally large subsets so that each values of one subset is lesser than the median value and each value of the other subset is equal or greater than the median value.

Pie chart and vertical bar chart
In a bar chart, you can represent the absolute or the relative frequency of a sample of data. The bars can be plotted vertically or horizontally. A pie chart always depicts the relative frequency of a sample set.

Boxplot
Another important graph is called "boxplot". It represents a number of important figures in one clear represenation. You already know the minimum, maximum and median values.
For a sample set, split by the median into two halves,

• the 1st quartile is the median of the lower half of the data,
• the 3rd quartile is the median of the upper half of the data.

A boxplot depicts the range of the values between the first and the third quartile as a box, containing a line indicating the median. The so called "whiskers" at both ends of the box show the minimum and maximum values. Sometimes, outliers are also shown in boxplots as isolated points.

The original image of the boxplot was provided by user RobSeb via Wikimedia Commons under license CC-BY-SA.

Variance and standard deviation
Last but not least there are two more key figures: the variance and the standard deviation, which measure the statistical dispersion of the sample set.

• Variance
  The variance s² is, in a population of samples, the mean of the squares of the differences between the respective samples and their mean:
  s^2 = \frac{1}{n} \sum_{i=1}^n (x_i - \overline x)^2
• Standard Deviation
  The standard deviation is the square root of the variance:
s = \sqrt{s^2} = \sqrt{\frac{1}{n} \sum_{i=1}^n (x_i - \overline x)^2}