Statistics - Median

 
   
     
       

Median

       

Understanding the Median in Statistics

       

          The Median is the middle value of an ordered dataset. It divides the dataset into two equal halves and is less affected by extreme values compared to the mean. It is especially useful in skewed distributions.        

        Median Graph      
     
       
         

Formula for Median:

         
           

              \[               x_{\text{median}} =               \begin{cases}                 x_{k+1}, & \text{if } n = 2k + 1 \quad \text{(odd number of values)} \\                 \frac{x_k + x_{k+1}}{2}, & \text{if } n = 2k \quad \text{(even number of values)}               \end{cases}               \]            

         
         

Where:

         
               
  • \(n\): Total number of values
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  • \(x_k, x_{k+1}\): \(k^{\text{th}}\) and \((k+1)^{\text{th}}\) ordered values
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  • The data must be arranged in ascending order
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Key Properties of Median:

         
               
  • Unaffected by extreme values (robust to outliers)
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  • Best for skewed or non-symmetric data
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  • Represents the 50th percentile (P50)
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  • Can be used for ordinal, interval, or ratio-level data
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Applications of Median:

         
               
  • Finding central income, house prices, or test scores
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  • Used in economics and finance for trend analysis
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  • Helpful in summarizing skewed data distributions
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  • Median filters in signal/image processing
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