Data Analysis and Statistics Fundamentals

Overview

Data analysis in MATLAB is about turning raw numbers into useful information. At this beginner level you will learn how to explore data, compute simple statistics, and prepare data for further analysis or modeling. MATLAB provides many built-in functions that make these tasks concise and reliable, so you can focus on interpreting results instead of reimplementing basic methods.

In this chapter you will get a conceptual overview of what you can do with data in MATLAB and how the different topics in this part of the course fit together. Detailed function usage, options, and advanced techniques are introduced in the child chapters.

Types of Data You Will Analyze

In MATLAB, data for analysis is usually stored in arrays, tables, or timetables. Numeric arrays represent measurements such as temperature readings or pixel intensities. Tables and timetables organize heterogeneous data where each column can have a different type and a name, which is common in experimental results, surveys, or financial data.

You might work with small arrays that you type directly, or larger datasets imported from CSV, Excel, or MAT files. Regardless of the source, the same basic ideas apply: you inspect the data, summarize it, look for patterns, and handle problems such as missing or inconsistent values.

Describing and Summarizing Data

Descriptive statistics provide quick numerical summaries of data. In MATLAB this typically involves computing quantities such as the mean, median, minimum and maximum, standard deviation, percentiles, and simple counts. For a numeric vector x, for example, functions like mean, median, and std return central tendency and spread.

In this part of the course you will learn how to compute these summaries for vectors, matrices, and table variables, and how to interpret them for practical questions. You will also see functions that generate a larger set of summary values at once and ways to combine numeric summaries with simple visualizations.

Sorting, Filtering, and Grouping

Once you know how to summarize data, the next step is to rearrange and subset it. Sorting rearranges observations according to one or more variables, so you can find top values, order records, or check for outliers. MATLAB offers functions that return sorted data, as well as the indices that describe how the original order changed.

Filtering selects only the rows or elements that satisfy certain conditions. This often uses logical indexing, which you already learn elsewhere in the course, combined with relational operators to build rules. For example, you might extract all rows where a measurement exceeds a threshold or where a category matches a particular label.

Grouping lets you apply operations by category, such as computing the mean value for each group defined by a categorical variable. In MATLAB this is especially convenient when working with tables and categorical arrays, where functions can automatically recognize groups and apply summaries per group.

Exploring Relationships with Correlation and Regression

Beyond describing single variables, data analysis often focuses on relationships between variables. Correlation measures how two variables vary together, and can help answer questions like whether higher input is associated with higher output. MATLAB provides functions that compute correlation coefficients and, when appropriate, correlation matrices across several variables.

Simple regression fits a line or another basic model to describe a relationship, typically between one predictor and one response. You will see how to run a basic regression, interpret its most important numeric outputs, and visualize fitted lines over data. At this beginner level the focus is on understanding the steps, not on advanced statistical theory.

Cleaning and Preparing Data

Real data often contains missing values, outliers, or inconsistencies. Before applying statistics or building models, you usually need to clean and prepare the data. In MATLAB, this involves identifying missing entries, deciding whether to remove or replace them, and making sure variable types are appropriate, for example numeric vs categorical.

You will learn simple techniques to detect problematic values, remove obviously invalid rows, and perform basic transformations like filling missing values with a constant or a simple estimate. More advanced cleaning methods exist, but this course starts with practical, straightforward approaches that are enough for many beginner projects.

Working with Time Based Data

Many datasets involve measurements taken over time, such as sensor readings, financial prices, or system logs. MATLAB has specialized support for time information. In this part of the course, you will learn how to represent time explicitly with datetime arrays and timetables, and how that helps with indexing and plotting.

Basic time series handling includes aligning data to regular time steps, calculating time differences, and aggregating values over intervals. Combined with plotting functions, this allows you to view trends and patterns over time, which is a very common requirement in both engineering and data science tasks.

Integrating Statistics with Visualization

Although this chapter focuses on numerical analysis, visualization plays an important supporting role. After computing summary statistics or fitting a simple regression, it is often useful to create quick plots to check assumptions, identify outliers, or communicate findings. MATLAB makes it straightforward to use the same data arrays for both numeric functions and plotting functions.

You will frequently move back and forth between computing numbers and drawing plots. For example, you might compute group means, then show them with a bar plot, or calculate a correlation and then overlay a regression line on a scatter plot. Later plotting chapters provide the detailed tools, while here you will see how visualization supports statistical reasoning.

Typical Beginner Workflow in MATLAB

A basic analysis session in MATLAB often follows a pattern. You start by loading or importing data into arrays or tables. Then you inspect the first few rows and basic size information to understand what you have. Next you compute descriptive statistics to get a sense of scale and variability. If needed, you clean the data by handling missing or strange values.

After that, you sort or filter to focus on relevant subsets, possibly grouping by categories to compare segments. You then explore relationships with correlation or a simple regression, and visualize key results. Finally, you save cleaned data or important results for later reuse.

As you progress through the child chapters in this section, each piece of this workflow will become concrete with MATLAB syntax, specific functions, and small example tasks, so that by the end you can carry out complete simple analyses on your own datasets.