Positional averages (or positional means) are statistical measures that depend on the position of values in an ordered dataset rather than mathematical computations like summation or multiplication. These averages are useful for understanding data distribution and are less affected by extreme values (outliers) than mathematical means.

Types of Positional Averages:

1. Median

• The middle value when data is arranged in ascending or descending order.
• If N (number of observations) is odd, the median is the middle value.
• If N is even, the median is the average of the two middle values.
• Formula for position: Median Position=(N+1)/2​
• Example:
  Data: 5, 10, 15, 20, 25 (N=5, odd) → Median = 15
  Data: 5, 10, 15, 20 (N=4, even) → Median = (10+15) / 2 = 12.5

2. Percentiles

• Divide a dataset into 100 equal parts, showing the relative standing of a value in the dataset.
• Example: The 90th percentile means that 90% of values are below it.

3. Quartiles

• Divide data into four equal parts:
  • Q1 (1st quartile) = 25th percentile (25% of data is below it).
  • Q2 (2nd quartile or Median) = 50th percentile.
  • Q3 (3rd quartile) = 75th percentile (75% of data is below it).

4. Deciles

• Divide data into 10 equal parts (similar to percentiles but in steps of 10%).
• D1 = 10th percentile, D5 = 50th percentile (Median), D9 = 90th percentile.

Key Differences:

Food for thought : Is Mode a Positional Average?

• Positional averages (like median, quartiles, and percentiles) are based on the position of values in an ordered dataset.

• Mode, however, does not depend on the position but on frequency (i.e., how often a value appears).