Statistical diagrams and graphs

Two teachers of a tutorial class conduct an analysis of the students’ performance in Chinese, English and Mathematics in order to evaluate the effectiveness of the course. They first organize and analyze a set of data with the stem-and-leaf diagram. They point out that the diagram is used for a small number of data and the original data can be retained in the diagram. To compare two different set of data of the same nature, they propose the use of a back to back stem-and-leaf diagram. The programme introduces the use of a scatter diagram for exploring the correlation between two sets of data. In a scatter diagram, when the dots are distributed roughly along an ascending tendency, there is a positive correlation between the two sets of data. On the contrary, when the dots are distributed rough along a descending tendency, there is a negative correlation. However, when the dots scatter irregularly without a pattern, there is no obvious correlation. For discrete or non-continuous data, a stem-and-leaf canbe converted into a bar chart which can be further developed into a histogram for handling a large amount of continuous data. The properties of a histogram are elaborated. The use of a frequency distribution table and the meaning of class boundaries are explained. The construction of a histogram is then demonstrated. With the introduction of class marks, the mid-points of the classes, in a frequency distribution table, a frequency polygon or a frequency curve is developed. The polygon or curve can give a clearer picture of the frequency distribution of the data. Furthermore, a frequency distribution table can be developed to form a cumulative frequency distribution table which is then used to construct a cumulative frequency polygon or curve. The last part of the programme encourages the enquiry on the differences in nature of the various diagrams/graphs and the selection of the appropriate diagrams/graphs to present a given set of data.