Stem-and-Leaf Displays and Mode

Lesson 06 of STA301 introduces exploratory data analysis techniques and begins the systematic investigation of Measures of Central Tendency. The lecture examines the Stem-and-Leaf display, a semi-graphical exploratory method pioneered by eminent statistician John W. Tukey in 1977. While traditional frequency tables and histograms group observations into anonymous tallies and discard raw numbers, the stem-and-leaf plot retains every individual numerical value. Each observation is separated into a 'stem' (the leading digit or digits) and a 'leaf' (the trailing digit). When arrayed horizontally, the display simultaneously presents the exact underlying numerical values and illustrates the visual shape, symmetry, spread, and modal clustering of the distribution. Building upon exploratory visualization, the lecture defines Measures of Central Tendency or statistical averages—single representative values that describe the central cluster of an entire dataset. According to statistical criteria formulated by George Udny Yule, a desirable average must be rigidly defined by mathematical formula, based on all observations, readily comprehensible, simple to compute, amenable to further algebraic manipulation, and minimally affected by extreme sampling fluctuations. The lecture investigates the Mode, defined as the most frequently occurring value in a dataset. For ungrouped data, the mode is determined by inspection, noting that datasets may be unimodal, bimodal, multimodal, or possess no mode if all values appear with equal frequency. For continuous grouped data, the mode resides within the modal class (the class interval exhibiting the highest frequency) and is calculated using the formula Mode = L + [fm - f1] / [(fm - f1) + (fm - f2)] * h, where L is lower class boundary, fm is modal frequency, f1 and f2 are preceding and succeeding frequencies, and h is class width. In Virtual University midterm evaluations, questions test modal formula computations, identifying modal classes, and constructing stem-and-leaf plots. Studying sta301 solved mcqs and revising past paper problems ensures thorough exam preparation. In preparing for Virtual University assessments in STA301 Statistics and Probability, students should thoroughly review past paper subjective questions and verify key formulas relating to Stem-and-Leaf Displays and Mode.