Descriptive Statistics and Data Presentation
Descriptive statistics opens the DHSE Statistics paper: classifying a variable, building a frequency table, and choosing the diagram that answers the question asked. Typical items require converting inclusive classes to exclusive ones, computing class marks or frequency densities, or reading a value from an ogive.
Building the table
- A variable is measurable (marks, height); an attribute is categorical (blood group, gender). A discrete variable is countable; a continuous variable is measured, so it is grouped into classes.
- Class mark = (lower limit + upper limit)/2. Class width = upper boundary − lower boundary.
- For inclusive classes (10–19, 20–29) subtract 0.5 from lower limits and add 0.5 to upper limits to obtain boundaries.
- Cumulative frequency is a running total. The less-than ogive is plotted against upper boundaries, the more-than ogive against lower boundaries; their intersection locates the median.
Graphs
In a histogram, area is proportional to frequency, so unequal widths need frequency density = frequency ÷ width. A frequency polygon joins class marks at height equal to frequency. In a pie diagram the sector angle = (component ÷ total) × 360°.
Worked example
Classes 0–10 (f = 5), 10–20 (f = 12), 20–40 (f = 24). Widths are 10, 10, 20; frequency densities are 0.5, 1.2 and 1.2, so the last two bars are drawn to the same height although their frequencies differ.
Traps that cost marks
- Plotting an ogive at class limits instead of class boundaries.
- Using raw frequency as bar height when class widths are unequal.
- Treating the class mark as an end-point rather than a midpoint.
- Reporting a pie angle as a percentage without converting.