Median

Short Answer
The median is the middle value in a sorted list of numbers. It divides the data set into two equal halves.

Median

Definition

In statistics, the median is a measure of central tendency that represents the middle value of a dataset when arranged in ascending or descending order. It is less sensitive to extreme values (outliers) compared to the mean and is especially useful for skewed distributions. To find the median, the data points are first sorted, and then:

  • If the number of observations (n) is odd, the median is the middle value.
  • If n is even, the median is the average of the two middle values.

The median is used in various contexts, including income distribution, demographic studies, and statistical analysis where understanding the typical or middle value is crucial.

Median

Examples

Income Distribution:

  • In a group of five people earning $20,000, $30,000, $40,000, $50,000, and $60,000 annually, the median income is $40,000.
  • Test Scores:
    • In a class of 10 students who scored 65, 70, 72, 75, 80, 82, 85, 88, 90, and 95 on a test, the median score is 80.
  • Housing Prices:
    • In a neighborhood with home prices of $250,000, $300,000, $320,000, $350,000, and $500,000, the median home price is $320,000.

    • Median

    Further Reads

    Books:

    • "Statistics" by David Freedman, Robert Pisani, and Roger Purves
      • A comprehensive textbook covering statistical concepts, including measures of central tendency like the median.
    • "Practical Statistics for Data Scientists" by Peter Bruce and Andrew Bruce
      • Focuses on applying statistics to real-world data analysis, including discussions on central tendency measures.
  • Articles and Online Resources:
    • Investopedia: Understanding the Median
      • An article explaining how to calculate and interpret the median in statistical analysis.
    • Khan Academy: Central Tendency and Variability
      • Provides tutorials and examples on measures of central tendency, including the median.
  • Websites:
    • Statista
      • Offers statistical data, charts, and infographics, including median values for various economic and social indicators.
    • National Center for Education Statistics (NCES)
      • Provides educational statistics, including median scores and performance metrics for standardized tests.
  • Courses:
    • Coursera: Statistics with R Specialization
      • Includes modules on descriptive statistics, including the median, using the R programming language.
    • edX: Data Analysis for Life Sciences
      • Covers statistical concepts and methods, including central tendency measures like the median, applied to life sciences data.

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