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Economics · Ch 5 — Measures of Central Tendency

Computation of Median

5.3.1

Computation of Median

For an individual (ungrouped) series the median is found by sorting the data from smallest to largest and reading off the middle value.

Locating the position. The position of the median in the ordered array is:

Position of median=(N+12)th item\text{Position of median} = \left(\frac{N+1}{2}\right)^{\text{th}} \text{ item}

This formula gives the position, not the median itself; the median is then the size of the item at that position:

Median=size of (N+12)th item\text{Median} = \text{size of } \left(\frac{N+1}{2}\right)^{\text{th}} \text{ item}

Odd number of items. For 5, 7, 6, 1, 8, 10, 12, 4, 3 arranged as 1, 3, 4, 5, 6, 7, 8, 10, 12 (here N=9N = 9), the position is 9+12=5th\frac{9+1}{2} = 5^{\text{th}} item, so the median is 6. Half the scores are larger than 6 and half are smaller.

Think About It

Activities

  • Find the mean and median for all four series below. What do you observe?
SeriesX (Variable Values)MeanMedian
A1, 2, 3??
B1, 2, 30??
C1, 2, 300??
D1, 2, 3000??
  • Is the median affected by extreme values? What are outliers?
  • Is median a better method than mean? …