Statistics – Simplified Study Notes
1. What is Statistics?
Statistics is the science of collecting, organizing, analyzing, and interpreting data in order to
understand patterns or make decisions.
2. Why Statistics is Important
- Helps researchers understand data.
- Allows scientists to test ideas and hypotheses.
- Used in psychology, economics, medicine, politics, and everyday decision‑making.
3. Descriptive vs. Inferential Statistics
Descriptive Statistics:
- Summarizes and describes data.
- Examples: averages, graphs, percentages.
Inferential Statistics:
- Uses sample data to make conclusions about a larger population.
- Examples: hypothesis testing, predictions.
4. Variables
A variable is any characteristic that can take different values (age, height, income, test
score).
5. Independent vs. Dependent Variables
Independent Variable (IV): the variable the researcher changes or controls.
Dependent Variable (DV): the outcome that is measured.
Example: Studying effect of sleep on test scores.
- IV: hours of sleep
- DV: test score.
6. Qualitative vs. Quantitative Variables
Qualitative (Categorical): describe qualities or categories (gender, color, nationality).
Quantitative (Numerical): represent numbers or amounts (age, height, income).
7. Discrete vs. Continuous Variables
Discrete: countable values (number of students, number of cars).
Continuous: any value in a range (height, weight, time).
8. Levels of Measurement
Nominal: categories with no order (eye color, country).
Ordinal: categories with order but unequal spacing (rankings).
Interval: numeric scale with equal intervals but no true zero (temperature in °C).
Ratio: numeric scale with equal intervals and true zero (height, weight, income).
9. Percentiles
A percentile tells you the percentage of scores that fall below a given value.
Example: If you are in the 90th percentile, you scored higher than 90% of people.
10. Distributions
A distribution shows how often each value occurs in a dataset.
Types include:
- Frequency distributions
- Probability distributions
- Graphs such as histograms.
11. Shapes of Distributions
Symmetrical: both sides look similar (normal distribution).
Skewed Right: long tail on the right.
Skewed Left: long tail on the left.
12. Summation Notation (Σ)
Used to represent the sum of many numbers.
Example:
ΣX = sum of all values of X.
13. Linear Transformations
Changing a variable using addition, subtraction, multiplication, or division.
Example: converting temperatures or rescaling scores.
14. Logarithms
A logarithm answers the question: 'To what power must a base be raised to get a certain
number?'
Example:
log10(100) = 2 because 10² = 100.