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@ Leonardo Araujo
2025-02-22 22:09:56
Starting with the basics, #statistics is a branch of #mathematics that deals with collecting, analysing, interpreting, presenting, and organising #data. It provides a way to make sense of data, see patterns, and make decisions based on data analysis. Here's a brief overview of some fundamental concepts in statistics:
### 1. Types of Statistics
- **Descriptive Statistics**: Involves summarising and organising data so it can be easily understood. Common measures include mean (average), median (middle value), mode (most frequent value), variance (measure of how spread out numbers are), and standard deviation (average distance from the mean).
- **Inferential Statistics**: Involves making predictions or inferences about a population based on a sample. This includes hypothesis testing, confidence intervals, and regression analysis.
### 2. Types of Data
- **Qualitative Data** (Categorical): Data that describes qualities or characteristics that cannot be measured with numbers, such as colors, names, labels, and yes/no responses.
- **Quantitative Data**: Data that can be measured and expressed numerically, including age, height, salary, and temperature. It can be further divided into discrete data (countable items, like the number of students in a class) and continuous data (measurable items, like height).
### 3. Measures of Central Tendency
- **Mean**: The average of a data set, found by adding all numbers and dividing by the count of numbers.
- **Median**: The middle value when a data set is ordered from least to greatest; if there’s an even number of observations, it is the average of the two middle numbers.
- **Mode**: The most frequently occurring value in a data set.
### 4. Measures of Spread
- **Range**: The difference between the highest and lowest values in a data set.
- **Variance**: Measures how far each number in the set is from the mean and thus from every other number in the set.
- **Standard Deviation**: The square root of the variance, providing a measure of the spread of a distribution of values.
### 5. Probability
Probability measures the likelihood of an event occurring, ranging from 0 (impossible) to 1 (certain). Understanding probability is essential for inferential statistics and making predictions based on data.
### 6. Sampling and Data Collection
- **Population**: The entire group that you want to draw conclusions about.
- **Sample**: A subset of the population, selected for the actual study. It’s crucial for the sample to be representative of the population to make accurate inferences.
### 7. Hypothesis Testing
This is a method of making decisions or inferences about population parameters based on sample statistics. It involves:
- Formulating a null hypothesis (no effect) and an alternative hypothesis (some effect).
- Calculating a test statistic based on the sample data.
- Using the test statistic to decide whether to reject the null hypothesis in favor of the alternative.