Lecture 4 (Theory)

29 Setembro 2026, 09:30 • Yiu Lim LUI

Measures of Location and Position: Measures of location identify the center or typical value of a dataset (such as the mode, median, and mean),

Mode and Median Calculation: The mode represents the most frequent value across various distribution types and can be estimated for grouped data using King's formula; the median divides ordered data in half and uses cumulative relative frequencies when calculated for grouped data.

Mean Variations and Properties: The standard arithmetic mean is sensitive to extreme values, whereas geometric and harmonic means are better suited for growth rates and speeds, and weighted or grouped means adjust calculations using frequencies and assigned weights. Additionally, the mean features key algebraic properties including shift rules, scaling rules, and a zero sum of deviations.

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Lecture 3 (Practice)

23 Setembro 2026, 11:00 • Yiu Lim LUI

We reviewed Exercise 2.1 and used a computer to complete it.

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Lecture 3

22 Setembro 2026, 09:30 • Yiu Lim LUI

·  Distribution Shape and Skewness: Histograms, stem-and-leaf plots, and boxplots help determine if data is symmetric, right-skewed (positively skewed with a tail to the right), or left-skewed (negatively skewed with a tail to the left).

·  Kurtosis and Variation: Kurtosis measures tail extremity and peak height (leptokurtic, mesokurtic, or platykurtic), while variation describes how tightly or widely data values cluster around the center.

·  Quantiles and Percentiles: Quantiles, deciles, percentiles, and quartiles () split ordered datasets into equal segments to indicate a value's relative position within the sample.

·  Summary Statistics and Boxplots: The five-number summary (minimum, Q1, median, Q3, maximum) forms the basis of boxplots, which use the Interquartile Range (IQR=Q3-Q1) to identify data spread and flag potential outliers.

·  Comparative and Distribution Plots: Scatter plots display relationships between two numerical variables, time plots track temporal sequences or trends, and Q-Q plots check whether a dataset follows a theoretical distribution like the normal distribution.

·  Frequency and Cumulative Distributions: Frequency tables organize discrete and continuous variables using absolute frequencies, relative frequencies, and midpoints, while cumulative functions (ogives) map how observations accumulate across values or intervals.

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Lecture 2 (Practice)

16 Setembro 2026, 11:00 • Yiu Lim LUI

We reviewed the core concepts and completed exercises 1.9, 1.10, and 2.1 (a, b, and c). We also explored common databases.

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Lecture 2

15 Setembro 2026, 09:30 • Yiu Lim LUI

·  Descriptive Statistics Overview: Descriptive statistics focuses on presenting data using tables and graphs, and summarizing data using measures like the sample mean.

·  Categorical Data Representation: Categorical variables are typically summarized using frequency distribution tables, crosstabs, bar charts, and pie charts, while avoiding misleading 3D graphical representations.

·  Numerical Data Representation: Numerical variables use frequency distributions, cumulative distributions, and visual tools such as histograms, stem-and-leaf displays, and boxplots.

·  Histogram Construction Rules: Building histograms requires defining the number of classes using rules like Sturges' rule or the square root rule, calculating class width, and plotting contiguous bars without gaps to represent data density.

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