Statistics

Applied Statistics with Python refers to the practical use of statistical methods and Python programming to analyze, interpret, and visualize data. With its rich ecosystem of libraries and tools, Python enables statisticians, data scientists, and analysts to handle complex data sets, perform advanced statistical computations, and generate meaningful insights.

Python having built-in library “statistics” for basic statistical functions. below are some sample code :

import statistics

data = [10, 20, 30, 40, 50]

# Mean
print("Mean:", statistics.mean(data))                # Output: Mean: 30

# Median
print("Median:", statistics.median(data))            # Output: Median: 30

# Mode
data_with_mode = [1, 2, 2, 3]
print("Mode:", statistics.mode(data_with_mode))      # Output: Mode: 2

# Standard Deviation
print("Standard Deviation:", statistics.stdev(data))  # Output: ~15.81
1. Applications of Applied Statistics :

  1. Descriptive Statistics:

    • Summarizing data using measures like mean, median, mode, range, and standard deviation.

    • Visualizing data distributions with histograms, boxplots, and violin plots.

  2. Inferential Statistics:

    • Drawing conclusions about a population based on sample data.

    • Techniques include hypothesis testing (t-tests, ANOVA), confidence intervals, and p-values.

  3. Regression Analysis:

    • Building models to understand relationships between variables.

    • Includes linear regression, logistic regression, and polynomial regression.

  4. Time Series Analysis:

    • Analyzing temporal data to identify trends, seasonality, and cyclic patterns.

    • Techniques include ARIMA modeling and forecasting.

  5. Hypothesis Testing:

    • Testing assumptions about data (e.g., A/B testing).

    • Tools like scipy.stats enable t-tests, chi-square tests, and more.

  6. Clustering and Classification:

    • Grouping data points or categorizing them based on features.

    • Techniques include k-means clustering and decision tree classification.

2. Core Libraries for Applied Statistics :

  1. numpy:

    • Core numerical computing library for arrays and mathematical functions.

    • Enables basic statistical operations like mean, median, standard deviation, and variance.

  2. pandas:

    • Provides data manipulation and analysis tools.

    • Supports descriptive statistics, data wrangling, and handling of large datasets.

  3. matplotlib and seaborn:

    • Libraries for data visualization.

    • Create histograms, scatter plots, boxplots, and more to visually interpret data.

  4. scipy:

    • Offers advanced statistical functions, distributions, and hypothesis testing.

  5. statsmodels:

    • Specialized library for statistical modeling, regression, and time series analysis.

  6. sklearn (scikit-learn):

    • Primarily a machine learning library, but it includes tools for statistical operations like clustering, PCA, and cross-validation.

So let’s understand one by one application of statistics in detail…

Descriptive Statistics