Introducción a la Estadística

Introduction to Statistics

• Descriptive statistics summarizes and describes data.
• Inferential statistics uses samples to draw conclusions about a population.
• Data can be qualitative or quantitative.
• Qualitative data presents characteristics or categories.
• Quantitative data provides numerical measurements.
• Data can be represented in tables, charts, and graphs.

Data Collection

• Sampling methods include simple random, stratified, and cluster sampling.
• Simple random sampling gives each individual an equal chance of selection.
• Stratified sampling selects individuals proportionally from different strata.
• Cluster sampling selects intact groups or clusters.
• Non-sampling error involves issues like poorly worded questions or biased responses.
• Sampling error arises from differences between sample and population.

Measures of Central Tendency

• Mean is the average of all values.
• Median is the middle value when data is ordered.
• Mode is the most frequent value.
• Mean is sensitive to outliers.
• Median is robust against outliers.
• Mode is useful for categorical data.

Measures of Variability

• Range is the difference between highest and lowest values.
• Variance measures how spread out data is from the mean.
• Standard deviation is the square root of variance.
• Standard deviation represents the average distance from the mean.
• Variance and standard deviation are sensitive to outliers.
• Interquartile range (IQR) measures the spread of the middle 50% of the data.

Probability

• Probability is the chance of an event occurring.
• Probability values range from 0 to 1.
• Probability of a complementary event is 1 minus the probability of the event.
• Probability of disjoint events is the sum of their individual probabilities.

Normal Distribution

• Normal distribution is a bell-shaped curve.
• Normal distributions are symmetrical around the mean.
• Standard deviation determines the spread of the curve.
• Empirical rule describes the proportion of data within certain standard deviations of the mean.

Hypothesis Testing

• Hypothesis testing assesses if there is enough evidence to support or reject a claim.
• A null hypothesis proposes there is no effect.
• An alternative hypothesis proposes there is an effect.
• p-value represents the probability of observing data as extreme as or more extreme than the observed data, assuming the null hypothesis is true.
• Reject the null when the p-value is less than a predetermined significance level (e.g., 0.05).

Correlation and Regression

• Correlation measures the strength and direction of a linear relationship between two variables.
• Correlation coefficient ranges from -1 to +1.
• Regression analysis models the relationship between a dependent and an independent variable.
• Linear regression models the relationship using a straight line.
• Regression analysis predicts the value of the dependent variable based on the independent variable.
• Coefficient of determination (R-squared) represents the proportion of variance in the dependent variable explained by the independent variable.

Other important concepts

• Sampling distribution of means
• Central limit theorem
• Confidence intervals
• Chi-square test
• ANOVA
• Statistical significance
• Types of errors in hypothesis testing (Type I and Type II)

Este cuestionario cubre los fundamentos de la estadística, incluyendo estadísticas descriptivas e inferenciales. Aprenderás sobre la recopilación de datos, métodos de muestreo y medidas de tendencia central. ¡Pon a prueba tus conocimientos sobre cómo se utilizan los datos en la estadística!