Location Statistic

Mean

Average of the values. Sum the values and divide by the total number

$$\mu =\frac{{\sum }_{i=1}^N{x}_i}{N}$$

Median

Median is the middle value if the total number of values is odd. If the number of values if even it’s the average of the middle two values.

Mode

Most frequent values in the dataset. If all values occur once then there’s no mode. There can be more than one modes in a dataset.

Python implementation

from typing import Sequence
from collections import Counter
 
data = [1, 2, 55, 11, 3, 5, 8, 11, 23, 32]
 
 
def mean(data: Sequence[int | float]) -> int | float:
    return sum(data) / len(data)
 
 
def median(data: Sequence[int | float]) -> float:
    data = sorted(data)
    n = len(data)
    middle = n // 2
 
    if n % 2 == 0:
        return sum(data[middle : middle + 2]) / 2
 
    return data[middle]
 
 
def mode(data: Sequence[int | float]) -> list[int | float]:
    counts = Counter(data)
    max_count = max(counts.values())
    print(counts)
    modes = [num for num, count in counts.items() if count == max_count]
 
    if len(modes) == len(data):
        return []
    return modes
 
 

PostgreSQL implementation

Let’s say we have a table of health data. With the columns user_id, measure, measure_value, We can calculate the mean, median and mode of weight measurements with the following query.

select
  AVG(measure_value) as avg_weight,
  
  PERCENTILE_CONT(0.5) WITHIN GROUP (
    ORDER BY
      measure_value
  ) as median_weight,
  
  MODE() WITHIN GROUP (
    ORDER BY
      measure_value
  ) as mode_weight
from
  health.user_logs
where
  measure = 'weight';