Descriptive Statistics (PDF, PMF, CDF, KDE)

1. Quantiles are cut points that divide a sorted dataset into equal-sized groups. They tell you where a specific data point stands relative to the rest of the group. 2.Percentiles: Divide data into 100 groups (e.g., scoring in the 90th percentile means you performed better than 90% of people). 3. Quartiles: Divide data into 4 groups (25% each).Q1 (25th percentile): The median of the lower half.Q2 (50th percentile): The Median of the entire dataset.Q3 (75th percentile): The median of the upper half.2. Boxplot (Box-and-Whisker Plot)A boxplot is a visual summary of a dataset’s distribution based on its quartiles. It is excellent for spotting skewness and outliers. 4. The Box: Stretches from Q1 to Q3. The length of the box represents the Interquartile Range (IQR), which holds the middle 50% of your data. The Line Inside: Represents the Median (Q2).The Whiskers: Lines extending outside the box to show the minimum and maximum values (excluding outliers).Individual Dots: Any points sitting past the whiskers are flagged as Outliers (usually data points further than \(1.5 \times \text{IQR}\) away from the box) 5. Covariance measures how two variables change together. It tells you the direction of their linear relationship. Positive Covariance: Both variables move in the same direction (e.g., as study hours go up, exam scores go up).Negative Covariance: Variables move in opposite directions (e.g., as car speed goes up, travel time goes down).The Flaw: Covariance is unbounded (can be any number like -421 or +0.005). Because it depends entirely on the units of measurement (like meters vs. kilometres), you cannot use it to judge the strength of the relationship. 6. Correlation is the standardised version of covariance. It tells you both the direction AND the strength of the linear relationship between two variables. The Scale: It is always locked between -1 and +1.+1 (Perfect Positive): Variables move together perfectly in a straight line.-1 (Perfect Negative): Variables move opposite to each other perfectly in a straight line.0 (No Relationship): Changing one variable tells you nothing about the other. #statistics #correlation #datascience #dataanalytics #coding link of pdf : https://drive.google.com/file/d/1edN9LSbMP...