1.1: What is Statistics?
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Introduction to Statistics and Data
We live in a world driven by data. From the moment we wake up and check the weather app to the instant we scroll through our streaming feed, we are interacting with data systems. Understanding how to think about, collect, analyze, and draw conclusions from data is at the heart of statistics and helps us make better decisions in everyday life and in professional fields ranging from public health to business to environmental science.
What is Data?
Definition: Data
Data refers to recorded information about individuals, objects, or events. These pieces of information are typically collected through observation, measurement, or experimentation.
A single recorded value is referred to as an observation, and a group of related observations forms a dataset.
Examples: Datasets That Fit the Definition of Data
1. Student Enrollment Dataset
What it records: Information about students at a college or university.
Example variables: Student ID, Major, Credits completed, GPA, Enrollment status
Each observation: One student’s record for a particular semester.
2. Fitness Tracker Dataset
What it records: Daily activity data from a wearable device.
Example variables: Date, Step count, Active minutes, Resting heart rate, Calories burned
Each observation: One person’s activity summary for one day.
3. Restaurant Health Inspection Dataset
What it records: Health inspection results from restaurants in a city.
Example variables: Restaurant name, Date of inspection, Number of violations, Score (out of 100), Status (pass/fail)
Each observation: One inspection event at a single restaurant.
4. Used Car Listings Dataset
What it records: Listings for vehicles posted on a used car website.
Example variables: Make and model, Year, Mileage, Listed price, City
Each observation: One vehicle currently listed for sale.
What is Statistics?
Definition: Statistics
Statistics is the science of learning from data in the presence of variation. It provides tools and methods for collecting, organizing, visualizing, analyzing, and interpreting data in order to make decisions, test hypotheses, and better understand the world.
Statistics is more than just "number crunching." It is a process that helps us make sense of information and uncertainty by understanding how the data were collected, what patterns they reveal, and whether those patterns are likely to be meaningful or due to chance.
Working with Data
When working with data, we usually follow a cycle that includes:
- Asking a question that can be answered with data
- Collecting accurate and relevant data
- Organizing and summarizing the data to understand its structure
- Analyzing the data to find patterns or test relationships
- Interpreting the results in context
- Communicating findings clearly and effectively
Data doesn’t speak for itself it needs interpretation and responsible analysis.
Descriptive vs. Inferential Statistics
Descriptive statistics help us summarize and understand the data right in front of us (like averages, medians, and graphs).
Inferential statistics help us go further making predictions or generalizations about a larger population based on sample data.
What's Next?
In the next section, we’ll take a closer look at two basic ways to describe variables in a dataset. Some variables describe qualities, labels, or categories, while others measure counts, measurements, or amounts. Developing an understanding of these fundamental categories categorical and quantitative variables will help us decide which statistical tools are appropriate for different types of data.