Update pages/2_Introduction_to_Statistics.py

pages/2_Introduction_to_Statistics.py

@@ -85,3 +85,93 @@ st.subheader("Inferential Statistics")
 st.markdown("""
     Inferential statistics involve making predictions or inferences about a population based on a sample. These methods are used to test hypotheses and estimate population parameters.
 """, unsafe_allow_html=True)
+
+st.title("Types of Statistics")
+
+# Descriptive Statistics
+st.header("1. Descriptive Statistics")
+st.markdown("""
+Descriptive statistics are used to summarize and describe the features of a dataset. They can be further divided into:
+""")
+
+# Measures of Central Tendency
+st.subheader("1.1 Measures of Central Tendency")
+st.latex(r"""
+\textbf{Measures of Central Tendency:} \\
+\text{These measures describe the center or typical value of a dataset.}
+""")
+st.latex(r"""
+\text{Mean:} \quad \bar{x} = \frac{1}{n} \sum_{i=1}^{n} x_i
+""")
+st.latex(r"""
+\text{Median:} \quad \text{The middle value in a sorted dataset}
+""")
+st.latex(r"""
+\text{Mode:} \quad \text{The most frequently occurring value in a dataset}
+""")
+
+# Measures of Dispersion
+st.subheader("1.2 Measures of Dispersion")
+st.latex(r"""
+\textbf{Measures of Dispersion:} \\
+\text{These measures describe the spread or variability of data points.}
+""")
+st.latex(r"""
+\text{Range:} \quad R = \text{Maximum value} - \text{Minimum value}
+""")
+st.latex(r"""
+\text{Variance:} \quad \sigma^2 = \frac{1}{n} \sum_{i=1}^{n} (x_i - \bar{x})^2
+""")
+st.latex(r"""
+\text{Standard Deviation:} \quad \sigma = \sqrt{\frac{1}{n} \sum_{i=1}^{n} (x_i - \bar{x})^2}
+""")
+
+# Data Distributions
+st.subheader("1.3 Data Distributions")
+st.latex(r"""
+\textbf{Data Distributions:} \\
+\text{These describe how data points are spread across different values.}
+""")
+st.latex(r"""
+\text{Normal Distribution (Gaussian):} \quad \mathcal{N}(\mu, \sigma^2)
+""")
+st.latex(r"""
+\text{Uniform Distribution:} \quad \text{All outcomes are equally likely}
+""")
+st.latex(r"""
+\text{Binomial Distribution:} \quad \text{Describes the number of successes in a fixed number of independent Bernoulli trials}
+""")
+
+# Inferential Statistics
+st.header("2. Inferential Statistics")
+st.markdown("""
+Inferential statistics make predictions or inferences about a population based on a sample of data. Key techniques include:
+""")
+
+st.subheader("2.1 Hypothesis Testing")
+st.latex(r"""
+\textbf{Hypothesis Testing:} \\
+\text{Involves testing a hypothesis about a population parameter.}
+""")
+st.latex(r"""
+H_0: \text{Null Hypothesis} \\
+H_1: \text{Alternative Hypothesis}
+""")
+
+st.subheader("2.2 Confidence Intervals")
+st.latex(r"""
+\textbf{Confidence Intervals:} \\
+\text{Provides a range of values within which the true population parameter is likely to fall.}
+""")
+st.latex(r"""
+\text{Confidence Interval:} \quad \bar{x} \pm Z_{\alpha/2} \frac{\sigma}{\sqrt{n}}
+""")
+
+st.subheader("2.3 Regression Analysis")
+st.latex(r"""
+\textbf{Regression Analysis:} \\
+\text{Examines the relationship between a dependent variable and one or more independent variables.}
+""")
+st.latex(r"""
+\text{Simple Linear Regression:} \quad y = \beta_0 + \beta_1 x + \epsilon
+""")