STATISTICSDescriptive StatisticsStatistics Calculator
๐Ÿ“Š

Minimum and Maximum Calculator

Free min max calculator. Find minimum, maximum, range, argmin, argmax, k-th smallest/largest. Runnin

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Why This Statistical Analysis Matters

Why: Statistical calculator for analysis.

How: Enter inputs and compute results.

min
STATISTICSDescriptive Statistics

Min, Max, Range โ€” k-th Smallest/Largest, Running Min/Max

Find minimum, maximum, range, positions (argmin/argmax), k-th order statistics, relative positions, and running min/max for time series.

Five Number Summary โ†’Least to Greatest โ†’

Real-World Scenarios โ€” Click to Load

Data โ€” comma or space separated

1 to 10
minmax_results.sh
CALCULATED
$ minmax --data="10 values" --k=1
Min
65.0000
Max
95.0000
Range
30.0000
argmin
5
argmax
8
1-th smallest
65.0000
1-th largest
95.0000
Share:
Min/Max Result
n = 10 values
Min: 65.00 | Max: 95.00
Range: 30.00argmin: 5argmax: 8
numbervibe.com/calculators/statistics/minimum-maximum-calculator

Data Bar Chart โ€” Min/Max Highlighted

Running Min/Max Line Chart

Relative Positions (valueโˆ’min)/(maxโˆ’min)

Calculation Breakdown

COMPUTATION
Min
65
Smallest value in data
Max
95
Largest value in data
Range
30
max โˆ’ min = 95 โˆ’ 65
argmin (positions)
5
Indices where min occurs
argmax (positions)
8
Indices where max occurs
2nd smallest
70
X_(2) = sorted[1]
2nd largest
92
X_(nโˆ’1) = sorted[nโˆ’2]
ORDER STATISTICS
k-th smallest (k=1)
65
X_(k) = sorted[kโˆ’1]
k-th largest (k=1)
95
X_(nโˆ’k+1) = sorted[nโˆ’k]
Running min/max
Tracked for each position
At i: min(data[0..i]), max(data[0..i])

For educational and informational purposes only. Verify with a qualified professional.

Key Takeaways

  • Min = smallest value; Max = largest value
  • Range = max โˆ’ min โ€” measures total spread
  • argmin/argmax โ€” positions (indices) where min/max occur
  • k-th smallest/largest โ€” order statistics (k=1 gives min/max)
  • Relative position = (value โˆ’ min) / (max โˆ’ min) โ€” 0 to 1 scale
  • Running min/max โ€” track best/worst value seen so far at each position

Did You Know?

๐Ÿ“ŠMin and max are the 1st and nth order statistics. The k-th smallest is the k-th order statistic.Source: Wikipedia Order Statistics
โš ๏ธMin and max are highly sensitive to outliers โ€” one extreme value can dominate the range.Source: NIST Handbook
๐Ÿ“For duplicate min/max, argmin and argmax list all positions where they occur.Source: Python docs
๐Ÿ”Running min is the smallest value seen so far; running max is the largest seen so far.Source: Time series analysis
๐Ÿ“ˆRelative position (valueโˆ’min)/(maxโˆ’min) normalizes data to [0, 1] for comparison.Source: Min-max normalization
๐Ÿ“‰The median is the (n+1)/2-th smallest (and largest) when n is odd.Source: Order statistics

Expert Tips

Duplicate Handling

When min or max appears multiple times, argmin/argmax list all positions. Count gives frequency.

Order Statistics

k=1: min, max. k=2: 2nd smallest, 2nd largest. k=(n+1)/2: median (odd n).

Running Stats

Useful for time series: track best/worst so far, detect new records (52-week high/low).

Normalization

Relative position (min-max normalization) scales data to [0,1] for ML or comparison.

Formulas Reference

Range = max โˆ’ min

k-th smallest = X_(k) = sorted[kโˆ’1]

Relative position = (x โˆ’ min) / (max โˆ’ min)

Frequently Asked Questions

What is argmin?

argmin is the position (index) where the minimum value occurs. If min appears multiple times, argmin lists all positions.

What is the k-th smallest?

After sorting, the k-th smallest is the value at position k (1-based). k=1 gives the minimum.

What is running min?

At each position i, running min is the smallest value among the first i+1 data points.

When is range zero?

When all values are equal. Min = max, so range = 0. Relative position is undefined.

How do I find the second smallest?

Set k=2. The 2nd smallest = sorted[1] (0-based) or the 2nd order statistic.

Applications

Time Series

Running min/max track records. Stock prices: 52-week high/low.

Sports

Best/worst times, scores. Position of record (argmin/argmax).

Machine Learning

Min-max normalization for feature scaling. Relative position in [0,1].

Quality Control

Specification limits. Min/max of measurements. Range for variability.

Order Statistics Quick Reference

kk-th Smallestk-th Largest
1MinMax
22nd smallest2nd largest
(n+1)/2Median (odd n)Median (odd n)
nMaxMin

Note: Min and max are sensitive to outliers. For robust analysis, consider IQR or median-based measures.

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