Modeling Data Distributions(KA/SAP/U4ModelingDataDistributions)

-

Unit 4: Modeling Data Distributions

Topics Covered:
  • Percentiles
  • Z-scores
  • Effects of linear transformations
  • Density curves
  • Normal distributions and the empirical rule
  • Normal distribution calculations
  • More on normal distributions

Percentiles

Explanation:
A percentile is a measure used in statistics indicating the value below which a given percentage of observations in a group of observations falls. For example, the 25th percentile is the value below which 25% of the observations may be found. Percentiles are useful for understanding the relative standing of a value within a data set.

Quiz:

Z-scores

Explanation:
A z-score tells you how many standard deviations a value is from the mean. It is calculated as z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation. Z-scores allow comparison between different data sets and help identify outliers.

Quiz:

Effects of Linear Transformations

Explanation:
Linear transformations involve adding, subtracting, multiplying, or dividing each value in a data set by a constant. Adding or subtracting changes the mean but not the standard deviation. Multiplying or dividing changes both the mean and the standard deviation by that factor.

Quiz:

Density Curves

Explanation:
A density curve is a smooth curve that shows the overall shape of a distribution. The area under the curve represents the total probability (which is 1). Density curves help us understand probabilities and proportions in continuous data.

Quiz:

Normal Distributions and the Empirical Rule

Explanation:
The normal distribution is a symmetric, bell-shaped curve. The empirical rule (68-95-99.7 rule) states that for a normal distribution:

  • About 68% of the data falls within 1 standard deviation of the mean
  • About 95% within 2 standard deviations
  • About 99.7% within 3 standard deviations

Quiz:

Normal Distribution Calculations

Explanation:
Calculating probabilities and percentiles for normal distributions often involves using z-scores and standard normal tables. You can find the probability that a value falls below, above, or between certain points using these tools.

Quiz:

More on Normal Distributions

Explanation:
Not all data sets are perfectly normal, but many real-world phenomena approximate a normal distribution. Skewness, kurtosis, and outliers can affect how closely a data set follows a normal curve. Understanding these deviations helps in better data analysis.

Quiz:

Comments

Post a Comment

Popular posts from this blog

🧠 Building a Korean Character Recognition Model with PyTorch

-
Image
Hangul, the Korean writing system, is both elegant and systematic. Each character is a combination of components called Jamo: 초성 (initial), 중성 (medial), and 종성 (final). In this project, I built a deep learning model using PyTorch to recognize these components from rendered character images. Here's how I did it. ✨ Project Overview This project involves: Generating synthetic images of Hangul characters with their bounding boxes. Decomposing characters into Jamo components. Training a convolutional neural network to classify each character's 초성, 중성, and 종성. Performing inference on single or multiple images and visualizing the results. Let’s break it down. 🏗️ Step 1: Generate Hangul Character Dataset We use a TrueType font (like Malgun Gothic ) to render images of Hangul syllables and compute their bounding boxes. Each image is saved along with Jamo annotations in JSON. generate_korean_chars.py from PIL import Image , ImageDraw , ImageFont import os i...
Read more

🍓 Fun Fruit Math Game for Kids – Learn Multiplication & Division with Smiles!

-
Image
🍓 Fruit Math Game 🍌 Check 🍓 Fun Fruit Math Game for Kids – Learn Multiplication & Division with Smiles! Learning math can be fun—especially when fruits and emojis get involved! 🎉 If you're looking for a simple, colorful way to help elementary school students practice multiplication and division, this interactive Fruit Math Game is perfect for you. 👶 Who's it for? This game is designed for: Elementary school students (Grades 1–3) Kids just starting to learn multiplication and division Parents or teachers looking for fun math learning tools 🧠 What does it teach? The game randomly generates problems for: Multiplication (e.g. 3 × 2) Division (e.g. 12 ÷ 4) Instead of just numbers, it uses fruit emojis like 🍎🍌🍓 to make math more visual and engaging. ✨ Key Features Colorful fruit emojis Randomized math problems Instant feedback (correct or try again!) Kid-friendly design 🖥️ How to Use Copy th...
Read more

Visualize Permutations and Combinations with Fruits!

-
Image
Fruit Permutation & Combination Visualizer Select number of fruits (n): Generate 🍎 Apple 🍌 Banana 🍇 Grapes 🍓 Strawberry 🍍 Pineapple Combinations (order doesn't matter) Permutations (order matters) Have you ever wondered how many different ways you can arrange fruits when choosing some from a basket? Today, let’s explore permutations and combinations with a fun and simple program using fruit emojis! 🍏 What You Will Learn The difference between permutations and combinations How to calculate them How to see them visually using fruit icons! 🥧 Meet the Fruits We have five fruits in our basket: 🍎 Apple 🍌 Banana 🍇 Grapes 🍓 Strawberry 🍍 Pineapple You can choose any number of fruits from 1 to 5. Once you choose, the program shows you: All combinations (order doesn’t matter) All permutations (order ma...
Read more