Frequency Distribution of Continuous Variables

Lesson 04 of STA301 focuses on the mathematical construction and graphical representation of continuous frequency distributions. When dealing with large volumes of continuous quantitative measurements—such as weights, test scores, or financial revenues—data must be grouped into orderly class intervals to reveal the underlying distributional pattern. The grouping process requires precise statistical terminology: Class Limits represent the nominal minimum and maximum stated values within a class (Lower Class Limit and Upper Class Limit); Class Boundaries denote the true mathematical limits that eliminate continuity gaps between adjacent classes, formed by subtracting and adding half the unit of measurement to stated limits; Class Mark or Mid-Point represents the central value of an interval, computed as the arithmetic average of class boundaries or class limits; and Class Width or Interval Size (h or c) represents the difference between successive lower class boundaries. To construct an optimal frequency distribution, students learn Sturges' Rule (k = 1 + 3.322 log10(n)), providing an objective mathematical guideline for determining the appropriate number of classes k for a sample size n. Once class width is established by dividing the data range by k, individual data points are tallied across non-overlapping intervals to produce the grouped frequency table. The lecture extensively covers the graphical representation of continuous frequency distributions through the Histogram—a set of adjacent, contiguous rectangles whose widths correspond to class boundaries and whose areas are strictly proportional to class frequencies. When class widths are unequal, frequency densities (frequency divided by class width) must be plotted on the vertical axis to maintain area proportionality. Students also learn the Frequency Polygon, formed by plotting class frequencies against class mid-points and connecting points with straight line segments tied down to the horizontal axis. For Virtual University midterm examinations, class boundary calculations, mid-point derivations, and histogram construction rules constitute high-yield topics. Diligent practice with sta301 short notes and solved past papers guarantees comprehensive exam preparation.