statistics 1.0-1.3

Definition: Statistics is the science of gathering, organizing, and analyzing data to make sense of the world. Think of it like reading reviews before buying a new skincare product to decide if it actually works.

Raw Data: The messy, unorganized list of every single purchase made at a boutique in a day.
Descriptive Statistics: Summarizing that data—for example, saying "the average spend per customer was $\$45$ " or creating a pie chart of the most popular nail polish colors.

Population ( $N$ ): The entire group you care about.
- Example: Every single person who uses the "Sol de Janeiro" perfume.
Sample ( $n$ ): A small group picked from that population.
- Example: 50 girls you found on TikTok who posted a review of the perfume.

Inferential Statistics: Taking what you learned from the 50 TikTok reviews (sample) and assuming that everyone in the world (population) probably feels the same way.
Representative Sample: If you want to know what all girls think of a brand, you can't just ask girls who only shop at luxury stores; you need a mix of people to represent the whole group accurately.

Parameter: A number describing the whole population (usually impossible to know perfectly).
- Example: The average amount of money ( $\mu$ ) all women in the U.S. spend on hair care annually.
Statistic: A number describing just your sample.
- Example: The average amount of money ( $\bar{x}$ ) spent on hair care by the 20 girls in your sorority.

Qualitative (Categorical): Descriptive traits.
- Example: Your favorite aesthetic (e.g., "Clean Girl," "Coquette," "Streetwear") or your zodiac sign.
Quantitative (Numerical): Numbers you can do math with.
- Discrete: Things you count. Example: The number of Stanley cups you own (you can't own 2.5 cups).
- Continuous: Things you measure. Example: The exact weight in grams ( $g$ ) of a blush compact or the height ( $cm$ ) of your favorite platform heels.

Cost & Time: You can't interview every girl on Earth about her favorite lip gloss; it would take forever and cost a fortune.
Destructive Testing: Imagine testing if a batch of waterproof mascaras is truly waterproof. If you open and test every single tube in the factory, you have nothing left to sell to customers!

Simple Random Sample: Putting the names of everyone who entered a giveaway into a hat and picking one blindly.
Stratified Sampling: Dividing your followers into groups by their hair type (Curly, Straight, Wavy) and then randomly picking 5 girls from each group to test a new shampoo.
Cluster Sampling: Dividing a city into neighborhoods (clusters), picking 3 neighborhoods at random, and surveying every girl in those 3 specific areas about their favorite cafe.
Convenience Sampling: Just asking your three best friends their opinion. It’s easy, but it’s biased because they probably think just like you do!

Misleading Graphs: A makeup brand might show a bar graph where their sales look 10x higher than a competitor's, but if you look closely at the vertical axis, the numbers start at 90 instead of 0 to make the gap look huge.
Self-Selected Bias: Looking at reviews on a website. Only the people who absolutely loved the product or absolutely hated it usually leave reviews, so the "4.5 star rating" might not represent the average person's experience.