Subjects

Stats and Prob

•

Dec 10, 2025

•

6 pages

Statistics Basics: Lessons 1 to 3 for SHS Students

Reigh<3

@reigh0fsunshine

Statistics is basically the science of collecting and making sense... Show more

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Reigh's
Notes
STATISTICS
Statistics and
Probability
SMTWTFS
- the science of conducting studies to collect,
organize, analyze, summarize, an

What is Statistics?

Think of statistics as your toolkit for handling data - it's how we collect, organize, analyze, and draw conclusions from numbers. You'll use these skills everywhere, from understanding poll results to analyzing your own academic performance.

There are two main types of statistics you need to know. Descriptive statistics help you describe what's happening right now - like finding the average grade in your class or creating charts to show data patterns. Inferential statistics go a step further by helping you make predictions and draw conclusions about larger groups based on smaller samples.

Understanding the difference between population (everyone you're studying) and sample (the smaller group you actually collect data from) is crucial. For example, if you want to know about all Grade 11 students in the Philippines, that's your population - but you might only survey students from a few schools as your sample.

Quick Tip: Variables can be qualitative (like favorite subjects or colors) or quantitative (like test scores or heights). Knowing which type you're working with determines how you'll analyze your data.

Types of Variables and Measurement Levels

Discrete variables deal with specific, countable numbers - think of things you can list out exactly like the number of siblings you have or books on a shelf. Continuous variables involve measurements that can have infinite possibilities, like your exact height, weight, or the time it takes to run a kilometer.

The level of measurement determines what you can do with your data. Nominal level is just categorizing (like school subjects or blood types) with no ranking involved. Ordinal level adds ranking but without precise differences - think grade levels or satisfaction ratings from "poor" to "excellent."

Interval level gives you precise differences between measurements but no true zero point (like temperature in Celsius). Ratio level has everything interval has plus a meaningful zero point (like your quiz scores or income).

Remember: The measurement level determines which statistical methods you can use - you can't calculate a meaningful average for nominal data like favorite colors!

Mean and Median Calculations

The mean (average) is your most reliable measure because it considers every single data point in your set. Use the formula X̄ = ΣX/n where you add up all values and divide by how many numbers you have. For example, with test scores 56, 35, 12, 20, 14, 28, 15, you'd get (56+35+12+20+14+28+15)/7 = 25.71.

The median finds the middle value and isn't easily thrown off by extreme scores. First, arrange your data in order from smallest to largest. Then use the formula $n+1$ /2 to find which position holds your median.

With an odd number of data points, you'll get a whole number that points directly to your median. With an even number of data points, you'll get a decimal (like 3.5th position), which means you average the two middle values.

Pro Tip: Median is super useful when you have outliers - like if one person scored 100 while everyone else scored around 75, the median gives you a better picture than the mean.

Mode and Data Set Classifications

Mode is the easiest measure to find - just look for the number that appears most often in your data set. Unlike mean and median, mode works perfectly with both numerical and categorical data (like finding the most popular subject among students).

Your data sets get classified by how many modes they have. Unimodal means one most frequent value, bimodal means two values tie for most frequent, and trimodal means three values appear most often. When you have four or more modes, call it polymodal or multimodal.

Sometimes you might have no mode at all - this happens when every value appears the same number of times. Other times, especially with categorical data like favorite movies or sports teams, mode might be your only meaningful measure of central tendency.

Real-world Application: Mode is perfect for business decisions - like which pizza flavor to stock most of, or which class schedule time slots are most popular with students.

Discrete Probability Distribution

Discrete probability distribution shows you all possible outcomes of a random variable and their chances of occurring. Think of it like a complete map of what could happen and how likely each possibility is.

Every probability distribution follows two essential rules. First, each probability must be between 0 and 1 (written as 0≤P(X)≤1) - you can't have negative chances or chances over 100%. Second, all probabilities must add up to exactly 1 (written as ΣP(X) = 1) because something has to happen.

The coin example shows this perfectly: when flipping three coins and counting tails, you could get 0, 1, 2, or 3 tails. Each outcome has its specific probability (1/8, 3/8, 3/8, 1/8), and notice how they all add up to 1.

Study Strategy: Practice identifying all possible outcomes first, then calculate their probabilities - this systematic approach prevents you from missing possibilities or making calculation errors.

Probability Distribution Tables and Histograms

Probability distribution tables organize your random variable values with their corresponding probabilities in a clean, easy-to-read format. This makes it simple to see patterns and verify that your probabilities follow the required rules.

Creating a histogram for probability distributions involves plotting random variable values on the horizontal axis and probabilities on the vertical axis. This visual representation helps you quickly identify which outcomes are most and least likely to occur.

The histogram becomes especially powerful when comparing different probability distributions or explaining your results to others. Bar heights immediately show probability differences, making complex statistical concepts much more accessible and understandable.

Visual Learning Tip: Always double-check that your histogram bars correspond to the correct probabilities in your table - visual accuracy is crucial for proper statistical interpretation.

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Subjects

Stats and Prob

•

Dec 10, 2025

•

6 pages

Statistics Basics: Lessons 1 to 3 for SHS Students

Reigh<3

@reigh0fsunshine

Visual Learning Tip: Always double-check that your histogram bars correspond to the correct probabilities in your table - visual accuracy is crucial for proper statistical interpretation.