Mathematical and Statistical Functions

One of NumPy's greatest strengths is its extensive library of built-in mathematical and statistical functions that operate directly on arrays efficiently and without loops.

Whether you are computing the average sales figure, finding the maximum temperature in a dataset, or applying a mathematical transformation to thousands of values at once, NumPy handles it all cleanly and quickly. 

Mathematical Functions

NumPy mathematical functions are called universal functions (ufuncs) — they apply element-wise across the entire array, making them fast and concise to use.

Basic Math Operations

These functions perform standard mathematical transformations on every element in an array simultaneously.

import numpy as np

arr = np.array([1, 4, 9, 16, 25])

print(np.sqrt(arr))       # Output: [1. 2. 3. 4. 5.]  — square root

print(np.square(arr))     # Output: [  1  16  81 256 625]  — square

print(np.abs(np.array([-3, -1, 2, -5])))  # Output: [3 1 2 5]  — absolute value

print(np.cbrt(arr))       # Output: cube root of each element

Exponential and Logarithmic Functions

These are widely used in data normalization, scaling, and statistical modeling.

A practical note: np.log() computes the natural logarithm (base e). If your analysis requires a different base, use np.log2() or np.log10() accordingly.

Trigonometric Functions

Useful in signal processing, physics-based data, and angular calculations. NumPy works in radians by default.

Rounding Functions

These functions are helpful when you need to control decimal precision in results.

arr = np.array([1.234, 2.567, 3.891, 4.105])

print(np.round(arr, 2))   # Output: [1.23 2.57 3.89 4.1 ]  — round to 2 decimals

print(np.floor(arr))      # Output: [1. 2. 3. 4.]  — round down

print(np.ceil(arr))       # Output: [2. 3. 4. 5.]  — round up

print(np.trunc(arr))      # Output: [1. 2. 3. 4.]  — remove decimals

Mathematical Functions

Statistical Functions

Statistical functions in NumPy allow you to summarize and understand your data quickly. These functions form the core of Exploratory Data Analysis (EDA) and are the building blocks behind Pandas' own statistical methods.

Descriptive Statistics

These are the most frequently used functions in data analysis, they give you an immediate snapshot of your dataset.

Variance and Standard Deviation

These functions measure how spread out the data is around the mean. A low standard deviation means values are close to the mean; a high one means they are widely spread.

By default, NumPy computes population variance and standard deviation. If you are working with a sample and need sample statistics, pass ddof=1.

Percentiles and Quantiles

Percentiles tell you the value below which a given percentage of data falls. This is essential in understanding data distribution and detecting outliers.

Axis-Based Statistics for 2D Arrays

When working with 2D data, such as a table of values — you often need statistics computed per row or per column rather than across the entire array.

Remembering the axis direction — axis=0 works down rows (column-wise) and axis=1 works across columns (row-wise) — will save you from common mistakes when analyzing tabular data.

Cumulative Functions

Cumulative functions compute running totals or running products, useful in financial data and time-series analysis.

Sorting and Ordering

NumPy also provides functions to sort arrays and retrieve the positions of sorted or extreme values, useful when you need ranked data.

data = np.array([42, 15, 78, 23, 56])

print(np.sort(data))          # Output: [15 23 42 56 78]  — sorted values

print(np.argsort(data))       # Output: [1 3 0 4 2]  — indices that would sort array

print(np.argmin(data))        # Output: 1  — index of minimum value

print(np.argmax(data))        # Output: 2  — index of maximum value

argsort() is particularly useful when you want to sort one array based on the order of another, a common requirement in data analysis.

Statistical Functions

Putting It All Together — Real-World Example

Consider a scenario where you have monthly revenue data and need a quick analytical summary.

This compact block of code delivers a complete business summary, something that would take significantly more effort using plain Python.