sum, mean, median, min & max

After an IPL season you have hundreds of numbers: runs in every match, balls faced, wickets. Nobody reads them one by one. A captain asks short questions — "How many runs did Virat score in total? What is his average? What was his best score?" Each answer collapses many numbers into one. In NumPy these are called aggregate functions (or reductions), and they run in fast C code instead of a Python loop.

Definition

An aggregate function (also called a reduction) takes an array of many values and reduces it to a smaller result — a single number for the whole array, or one number per row/column when you pass axis. The core ones are sum, mean, median, min and max.

• Reduces — the output has fewer elements than the input. 10 match scores go in, 1 total comes out.
• Whole array by default — with no axis, NumPy treats a 2D array as one big bag of numbers.
• Vectorized — the loop happens inside NumPy's compiled code, so arr.sum() on a million values is far faster than Python's for loop.

Syntax

Most aggregates come in two forms that do exactly the same thing:

np.sum(a, axis=None, dtype=None, keepdims=False)    # function form
a.sum(axis=None, dtype=None, keepdims=False)        # method form

np.mean(a, axis=None)      a.mean(axis=None)
np.min(a, axis=None)       a.min(axis=None)        # np.amin is an old alias
np.max(a, axis=None)       a.max(axis=None)        # np.amax is an old alias
np.median(a, axis=None)    # function form ONLY — there is no a.median()

Note: the function form np.sum(x) also works on a plain Python list (NumPy converts it first). The method form x.sum() only works when x is already a NumPy array.

Example — Virat's season in five numbers

import numpy as np

virat = np.array([72, 45, 88, 31, 64, 0, 103, 52, 19, 77])

print("Total runs :", virat.sum())
print("Average    :", virat.mean())
print("Median     :", np.median(virat))
print("Lowest     :", virat.min())
print("Highest    :", virat.max())
print("Matches    :", virat.size)

Total runs : 551
Average    : 55.1
Median     : 58.0
Lowest     : 0
Highest    : 103
Matches    : 10

How it works: sum adds all 10 scores (551). mean divides that by the count (551 ÷ 10 = 55.1). median sorts the scores and takes the middle — with 10 values there are two middle values (52 and 64), so it averages them: 58.0. min and max pick the duck and the century.

Example — function form vs method form

import numpy as np

virat = np.array([72, 45, 88, 31, 64, 0, 103, 52, 19, 77])

print(np.sum(virat), virat.sum())     # same answer
print(np.max(virat), virat.max())     # same answer
print(np.sum([10, 20, 30]))           # function form accepts a plain list

print(type(virat.sum()))              # a NumPy integer scalar
print(type(virat.mean()))             # mean is always a float

551 551
103 103
60
<class 'numpy.int64'>
<class 'numpy.float64'>

How it works: both forms call the same C code. Notice the types: summing integers gives a NumPy integer (np.int64), but mean always returns a float (np.float64) because an average is usually not a whole number.

Mean vs median — why we need both

The mean is pulled towards extreme values; the median is not. Look at a batter who scored one big century and failed in the rest:

import numpy as np

scores = np.array([12, 8, 15, 10, 150])
print("mean  :", scores.mean())
print("median:", np.median(scores))

mean  : 39.0
median: 12.0

The mean (39.0) suggests he scores almost 40 every match — misleading. The median (12.0) says his typical innings is about 12. When data has outliers, report the median too.

Example — aggregates on 2D data

import numpy as np

# rows = players, columns = matches
scores = np.array([
    [72, 45, 88, 31, 64],   # Virat
    [56,  0, 74, 88, 32],   # Rohit
    [45, 32,  0, 67, 18],   # Hardik
    [33, 61, 45,  0, 77],   # Shubman
])

print("Squad total  :", scores.sum())
print("Squad average:", scores.mean())
print("Best score   :", scores.max())
print("Per player   :", scores.sum(axis=1))

Squad total  : 928
Squad average: 46.4
Best score   : 88
Per player   : [300 250 162 216]

How it works: without axis, the 4×5 table is treated as 20 numbers. With axis=1 you get one total per player (row). The axis parameter is so important that it has its own topic next.

Other useful aggregates

Note: in NumPy 2.x the method a.ptp() was removed — use the function np.ptp(a) or simply a.max() - a.min().

Common mistakes

• ❌ virat.median() → AttributeError: 'numpy.ndarray' object has no attribute 'median'. ✅ np.median(virat) — median has only a function form.
• ❌ Using Python's built-in sum(scores) on a 2D array — it adds the rows together and returns an array, not one number. ✅ Use scores.sum() or np.sum(scores).
• ❌ Using built-in max() / min() on big arrays — they loop in slow Python and fail on 2D arrays. ✅ Use arr.max() / arr.min().
• ❌ Reporting only the mean when there are outliers (one 150 among small scores). ✅ Check the median as well.
• ❌ Writing virat.sum without brackets — you get the method object, not the total. ✅ virat.sum().

Comparison — Python list vs NumPy

Interview tip

Q: Why is there arr.mean() but no arr.median()? A: The median needs a partial sort of the data, and NumPy only exposes it as the function np.median(). Functions like sum, mean, min, max, std, var, prod, argmin and argmax exist in both forms; median, percentile, quantile and ptp are function-only.