Array Statistics

easyPROArray MathematicsNumPy StatisticsNumpy

Problem Statement

Calculate basic statistics of a NumPy array.

Background

NumPy provides statistical functions:

np.sum(): Sum of elements
np.mean(): Average
np.min(), np.max(): Min and max
np.std(): Standard deviation

Your Task

Write a function array_stats(arr) that returns a dictionary with:

"sum": Sum of all elements
"mean": Mean (average), rounded to 2 decimals
"min": Minimum value
"max": Maximum value
"std": Population standard deviation (divide by $n$ , not $n-1$ ), rounded to 2 decimals

Output Format

Return a dictionary with exactly these five keys.

Example

Input

[1, 2, 3, 4, 5]

Output

{'sum': 15, 'mean': 3.0, 'min': 1, 'max': 5, 'std': 1.41}

Reasoning

Input: arr is a 1-D array of five integers, $x = (1, 2, 3, 4, 5)$ , so $n = 5$ .
Sum and mean: $\sum_i x_i = 1+2+3+4+5 = 15$ , and the mean is $\mu = 15 / 5 = 3$ , shown as 3.0 (a decimal, since averages are generally not whole).
Min and max: the smallest and largest entries are 1 and 5; like the sum, they stay whole numbers because every input is an integer.
Standard deviation: the deviations from the mean are $-2, -1, 0, 1, 2$ , whose squares are $4, 1, 0, 1, 4$ (total $10$ ). Dividing by $n = 5$ gives a variance of $2$ , so $\sigma = \sqrt{2} \approx 1.4142$ , which rounds to 1.41 at 2 decimal places.
Output: a dictionary with exactly the keys sum, mean, min, max, std.
Notice that dividing by $n - 1 = 4$ instead would give $\sqrt{2.5} \approx 1.58$ , which is not the expected answer. A constant array such as $(5, 5, 5, 5)$ has every deviation zero, so its std is 0.0.

Constraints

Round mean and std to 2 decimal places
Array will have at least 1 element

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1. Background Knowledge

NumPy arrays are the standard for efficient numerical computation in Python, enabling vectorized operations that avoid Python loops for high performance. Key statistical functions are built-in:

Sum: $\sum_{i=1}^n x_i$
Mean: $\mu =$ \frac{1}{n}\sum_{i=1} $^n x_i$
Min/Max: $\min(x) = x_{$ \text{min} $}, \max(x) = x_{$ \text{max} $}$
Standard Deviation: $\sigma = \sqrt{$ \frac{1}{n}\sum_{i=1} $^n (x_i -$ \mu $)^2}$ (population std by default in np.std)

Prerequisites: Basic NumPy array creation (np.array()), dictionary usage, and rounding (round(value, 2)).

2. Algorithm Approach

Use NumPy's optimized C-implemented functions for O(n) linear scans across the array—no custom loops needed. This leverages array programming paradigm: single function calls compute statistics via vectorization, minimizing operation counts and memory copies.

Direct mapping:

Statistic	NumPy Function
sum	np.sum(arr)
mean	np.mean(arr)
min	np.min(arr)
max	np.max(arr)
std	np.std(arr)

3. Step-by-Step Strategy

Import NumPy: import numpy as np
Define function: def array_stats(arr):
Compute statistics using built-in functions
Round mean/std: round(np.mean(arr), 2) and round(np.std(arr), 2)
Return dictionary: return {"sum":..., "mean":..., "min":..., "max":..., "std":...}

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