Central Tendency

Arithmetic Mean

Compute the arithmetic mean as the sum of all values divided by the count. The replay builds the running total step by step, then shows a second pass where each deviation v - mean accumulates into dev_sum, ending at 0 — demonstrating that the mean is the balance point of the distribution.

By hand

With the library

statistics.mean and numpy.mean both reduce the list to a single value. statistics.mean operates on pure Python sequences; np.mean works on any array-like and is vectorised for large datasets.

naive.py 
values = [4, 8, 6, 13, 10, 6, 8, 7]
total = 0
n = 0
for v in values:
    total = total + v
    n = n + 1
mean = total / n
dev_sum = 0
for v in values:
    dev_sum = dev_sum + (v - mean)
print('RESULT:', round(mean, 10))
library.py 
import statistics
import numpy as np
from dalib.display import set_display
set_display()

values = [4, 8, 6, 13, 10, 6, 8, 7]
mean_stdlib = float(statistics.mean(values))
mean_numpy = float(np.mean(values))
print('statistics.mean:', mean_stdlib)
print('np.mean:        ', mean_numpy)
print('RESULT:', round(mean_stdlib, 10))

statistics.mean: 7.75
np.mean:         7.75
RESULT: 7.75

Implementation notes

  • The deviations summing to zero is the defining property of the mean as a balance point: sum(v - mean for v in values) == 0 (up to float rounding). No other value has this property.
  • This lesson shares mechanics with python-data-basics/list-sum-mean; the framing there is algorithmic (how to compute it), while here it is statistical (what the result means).
  • statistics.mean returns int when the mean divides evenly for an all-integer input; float() normalises before printing.
  • For large arrays, prefer np.mean — it is vectorised and avoids Python loop overhead. Its internal summation order also tends to produce smaller rounding error than a scalar running total, though the exact behaviour depends on array shape and NumPy version.