The axis Parameter

Our squad data is a table: rows are players, columns are matches. "Total runs" is ambiguous here — do you mean each player's season total, each match's team total, or one grand total? The axis parameter is how you tell NumPy which one you want.

Definition

The axis parameter tells an aggregate function which dimension to collapse. The result has that dimension removed: axis=0 collapses the rows (giving one value per column), axis=1 collapses the columns (giving one value per row), and axis=None collapses everything into a single number.

• Collapse — the axis you name disappears from the shape. A (4, 5) array summed over axis=0 becomes (5,); over axis=1 it becomes (4,).
• axis 0 — the first index, scores[i, :] → moving down the rows.
• axis 1 — the second index, scores[:, j] → moving across the columns.

                axis 1  →  (across: match 1 … match 5)
              M1   M2   M3   M4   M5
 axis 0  Virat   [ 72,  45,  88,  31,  64 ]   → sum(axis=1) = 300
   ↓     Rohit   [ 56,   0,  74,  88,  32 ]   → sum(axis=1) = 250
 (down)  Hardik  [ 45,  32,   0,  67,  18 ]   → sum(axis=1) = 162
         Shubman [ 33,  61,  45,   0,  77 ]   → sum(axis=1) = 216
                   ↓    ↓    ↓    ↓    ↓
 sum(axis=0) =   206  138  207  186  191

Tip — the memory trick: "axis=0 goes down, axis=1 goes across." Or: the axis you pass is the one that gets squashed. Squash the rows (axis 0) → one answer per column (per match). Squash the columns (axis 1) → one answer per row (per player).

Syntax

a.sum(axis=None, keepdims=False)
a.mean(axis=0)            # one value per column
a.max(axis=1)             # one value per row
a.sum(axis=(0, 1))        # a tuple of axes = reduce several at once
a.sum(axis=-1)            # negative axis counts from the end (-1 = last axis)

Works for sum, mean, median, min, max, std, var, prod, argmin, argmax, percentile, cumsum and more.

Example — per player vs per match

import numpy as np

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("shape:", scores.shape)

print("Grand total          :", scores.sum())
print("Per player (axis=1)  :", scores.sum(axis=1), scores.sum(axis=1).shape)
print("Per match  (axis=0)  :", scores.sum(axis=0), scores.sum(axis=0).shape)
print("Best per player      :", scores.max(axis=1))
print("Avg per match        :", scores.mean(axis=0))

shape: (4, 5)
Grand total          : 928
Per player (axis=1)  : [300 250 162 216] (4,)
Per match  (axis=0)  : [206 138 207 186 191] (5,)
Best per player      : [88 88 67 77]
Avg per match        : [51.5  34.5  51.75 46.5  47.75]

How it works: axis=1 squashes the 5 match columns, leaving one number for each of the 4 players → shape (4,). axis=0 squashes the 4 player rows, leaving one number for each of the 5 matches → shape (5,).

Example — keepdims=True for broadcasting

Say you want each score as a percentage of that player's season total. Dividing a (4, 5) array by a (4,) array fails, because broadcasting lines shapes up from the right (5 vs 4). keepdims=True keeps the result as a (4, 1) column, which broadcasts perfectly:

import numpy as np

scores = np.array([
    [72, 45, 88, 31, 64],
    [56,  0, 74, 88, 32],
    [45, 32,  0, 67, 18],
    [33, 61, 45,  0, 77],
])

totals = scores.sum(axis=1, keepdims=True)
print("totals shape:", totals.shape)
print(totals)

share = scores / totals * 100
print(share.round(1))
print("each row adds up to:", share.sum(axis=1).round(1))

totals shape: (4, 1)
[[300]
 [250]
 [162]
 [216]]
[[24.  15.  29.3 10.3 21.3]
 [22.4  0.  29.6 35.2 12.8]
 [27.8 19.8  0.  41.4 11.1]
 [15.3 28.2 20.8  0.  35.6]]
each row adds up to: [100. 100. 100. 100.]

How it works: totals is a column (4, 1). Broadcasting stretches it across the 5 columns, so every score is divided by its own player's total. Without keepdims you would need totals[:, np.newaxis] or .reshape(-1, 1).

Example — 3D data and a tuple of axes

Add a third dimension: 2 seasons × 4 players × 5 matches. Now axis=0 means season, axis=1 means player, axis=2 (or -1) means match.

import numpy as np

seasons = np.arange(40).reshape(2, 4, 5)   # 2 seasons, 4 players, 5 matches
print("shape:", seasons.shape)
print("sum(axis=0) shape :", seasons.sum(axis=0).shape)       # combine seasons
print("sum(axis=-1) shape:", seasons.sum(axis=-1).shape)      # one total per season per player
print("per player, all seasons & matches:", seasons.sum(axis=(0, 2)))

shape: (2, 4, 5)
sum(axis=0) shape : (4, 5)
sum(axis=-1) shape: (2, 4)
per player, all seasons & matches: [120 170 220 270]

Common mistakes

• ❌ Thinking axis=0 means "per row". ✅ axis=0 collapses the rows, so you get one value per column.
• ❌ scores / scores.sum(axis=1) → ValueError: operands could not be broadcast together with shapes (4,5) (4,). ✅ Use keepdims=True.
• ❌ Passing axis=2 to a 2D array → AxisError: axis 2 is out of bounds for array of dimension 2. ✅ A 2D array only has axes 0 and 1 (or -1, -2).
• ❌ Forgetting axis and getting one grand total when you wanted per-player totals. ✅ Always ask: one number, one per row, or one per column?

Comparison — the three choices on a (4, 5) array

Interview tip

Q: For an array of shape (100, 3), what is the shape of a.mean(axis=0)? A: (3,) — axis 0 (the 100 rows) is collapsed, leaving one mean per column. In data-science terms: if rows are samples and columns are features, axis=0 gives the per-feature mean.