Probability & Statistics 1 · Representation of data
Display numerical data in stem-and-leaf diagrams, histograms, and cumulative frequency graphs.
Interpret statistical data presented in various forms.
Select an appropriate method for displaying data.
Distinguish between qualitative and quantitative data.
Differentiate between discrete and continuous quantitative data.
Calculate frequency density for histogram construction.
Estimate values from cumulative frequency graphs and histograms.
Compare different data representations for suitability.
Frequency density
Used for constructing histograms, especially with unequal class widths, to ensure column area is proportional to frequency.
Class frequency (from frequency density)
Used to calculate the frequency of a class when its frequency density and class width are known, often for estimating frequencies from a histogram.
Students often confuse histograms with bar charts, particularly regarding gaps between columns and the meaning of column height/area.
Students often use the given class limits (e.g., 146-150) directly for continuous data calculations, rather than correctly determining the class boundaries (e.g., 145.5-150.5).
Students often plot cumulative frequencies against class mid-values instead of upper class boundaries on cumulative frequency graphs.
Students often omit the key in stem-and-leaf diagrams, making the diagram uninterpretable.
Students often draw leaves in a back-to-back stem-and-leaf diagram incorrectly, failing to order them ascending outwards from the stem on both sides.
Students often assume that the class with the highest frequency in a histogram also has the highest frequency density, which is not necessarily true, especially with unequal class widths.