Functions & Algebra: Domain, Graphing, and Key Techniques
Function Basics
Definition: A function assigns exactly one output for each input.
Function notation: f(x)
Vertical Line Test: If any vertical line intersects a graph more than once, the relation is not a function.
Using Tables to Graph (by Hand)
Steps:
- Choose x-values (use symmetry if possible).
- Plug the x-values into the function.
- Create a table of (x, f(x)).
- Plot the points.
- Connect points smoothly to represent the graph.
Always check:
- x-intercepts
- y-intercept
- asymptotes (if any)
Domain Rules (Very Important)
Read MoreExcel Import, Cleaning, Transformation & Visualization
Importing and Exporting Data
In data science, importing is the act of bringing external data into Excel for analysis, while exporting is saving your Excel data into a format that other programs can read.
Common File Formats
Understanding these formats helps you choose the right one for your task:
- Excel Workbook (.xlsx): A workbook that stores data, formulas, formatting, charts, and multiple sheets. Best for your working file.
- CSV (Comma-Separated Values): A plain text file where a comma separates each
Essential Excel Data Analysis Techniques for Business
Data Management Fundamentals: Sorting and Filtering
1. Sorting: Putting Data in Order
Purpose: To rearrange your data in a specific sequence (like A to Z or High to Low) without removing anything.
Types of Sorting
- Alphabetical (A to Z or Z to A): Great for names, cities, or product types.
- Numerical (Smallest to Largest): Best for prices, ages, or quantities.
- Date (Oldest to Newest): Perfect for tracking timelines or schedules.
Sorting Example
Imagine you have a list of students and their test scores.
- Unsorted:
Mastering Essential Excel Functions for Data Analysis
Essential Excel Tools for Data Analysis
These tools allow you to connect different datasets and distill thousands of rows into a few meaningful numbers.
Lookup Functions and Data Summarization
1. VLOOKUP (Vertical Lookup)
This is the most common lookup function. Use it when your data is arranged in columns (vertically). It searches for a value in the leftmost column and looks to the right to find what you need.
The Syntax
=VLOOKUP(lookup_value, table_array, col_index_num, [range_lookup])
- lookup_value:
Statistical Inference Solutions: Estimation and Hypothesis Testing
Q1 True/False (each needs a quick justification)
Q1(a) Binomial(100, 0.2) approximated by Normal N(20,16)
Steps:
Identify: X ~ Bin(n=100, p=0.2).
Compute mean: μ = np = 100(0.2) = 20.
Compute variance: σ² = np(1−p) = 100(0.2)(0.8) = 16.
Rule: For large n, Binomial ≈ Normal with same mean/variance (CLT-ish approximation).
Conclusion: Yes, approximate with N(20,16).
Q1(b) MAP estimator equals argmax log posterior
Steps:
MAP definition: θ̂MAP = argmaxθ f(θ|x).
Taking log does not move the maximizer
Essential Templates for Data Visualization Reporting
Line Graph Analysis Template
- The line graph illustrates trends in [subject] over a [time period] from [start date] to [end date]. The data is measured in [units] and demonstrates [general observation].
- Overall, the most significant trend is the [adjective] [increase/decrease] in [main subject]. While [item A] showed substantial growth, [item B] experienced considerable fluctuation. The period witnessed [item C] consistently [outperforming/underperforming] other categories.
- Beginning with [item A],