STATISTICSDescriptive StatisticsStatistics Calculator
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Midrange Calculator

Free midrange calculator. Compute midrange, range, mean, median. Compare measures. Outlier sensitivi

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Why This Statistical Analysis Matters

Why: Statistical calculator for analysis.

How: Enter inputs and compute results.

MR
STATISTICSDescriptive Statistics

Midrange โ€” (Min + Max) / 2

Simple central tendency. Compare with mean, median, trimmed mean. See how outliers shift midrange vs median.

Real-World Scenarios โ€” Click to Load

Data Input

midrange_results.sh
CALCULATED
$ midrange --n=10
Min
65.0000
Max
95.0000
Midrange
80.0000
Range
30.0000
Mean
81.9000
Median
84.5000
Trimmed mean
82.3750
Breakdown point
0% (one outlier can destroy it)
Share:
Midrange
Midrange = 80.0000
80.000
Range: 30.00Mean: 81.90Median: 84.50
numbervibe.com/calculators/statistics/midrange-calculator

Data Plot with Min/Max Highlighted

Min/max highlighted. Midrange=80.00, Mean=81.90, Median=84.50.

Measure Comparison

Outlier Sensitivity Demo

Adding a high outlier: Midrange shifts from 78.50 to 110.00; Median shifts from 84.00 to 84.50.

Calculation Breakdown

COMPUTATION
Min
65.0000
ext{Smallest} ext{value}
COMPUTATION
Max
95.0000
ext{Largest} ext{value}
RESULT
Midrange
80.0000
(65.00 + 95.00) / 2
SPREAD
Range
30.0000
max โˆ’ min = 95.00 โˆ’ 65.00
COMPARISON
Mean
81.9000
\text{Sigma} x/n
COMPARISON
Median
84.5000
50th ext{percentile}
COMPARISON
Trimmed mean
82.3750
ext{Mean} ext{of} ext{middle} 80%
ROBUSTNESS
Breakdown point
0% (one outlier can destroy it)

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

Key Takeaways

  • โ€ข Midrange = (min + max) / 2 โ€” the midpoint of the data range
  • โ€ข Range = max โˆ’ min โ€” measures total spread
  • โ€ข Breakdown point 0%: One outlier can completely distort the midrange
  • โ€ข Compare: Mean, median, midrange, and trimmed mean for the same data
  • โ€ข Use case: Quick estimate when data is symmetric and outlier-free

Did You Know?

๐Ÿ“ŠThe midrange is the midpoint of the range โ€” equivalent to the average of the two extreme order statistics.Source: Order statistics
โš ๏ธMidrange has 0% breakdown point: a single extreme value can make it useless as a measure of center.Source: Robust statistics
๐Ÿ“For symmetric, uniform data, midrange equals the mean and median.Source: Distribution theory
๐Ÿ”Adding one high outlier shifts the midrange dramatically; the median barely moves.Source: Outlier sensitivity
๐Ÿ“ˆMidrange is rarely used in modern statistics due to its extreme sensitivity to outliers.Source: Best practice
๐Ÿ“‰Trimmed mean removes 10% from each tail โ€” a compromise between mean and median robustness.Source: Robust estimation

How It Works

1. Find Min and Max

Sort the data and take the smallest (min) and largest (max) values.

2. Compute Midrange

Midrange = (min + max) / 2. This is the arithmetic mean of the two extremes.

3. Compare with Mean and Median

Mean uses all values; median uses the middle; midrange uses only extremes. Compare to see outlier impact.

Mean vs Median vs Midrange vs Trimmed Mean

MeasureFormulaBreakdown PointUse Case
Meanฮฃx/n0%Symmetric, no outliers
Median50th percentile50%Skewed or with outliers
Midrange(min+max)/20%Quick estimate, symmetric
Trimmed meanMean of middle 80%~10%Compromise robustness

Frequently Asked Questions

What is the midrange?

Midrange = (min + max) / 2. It is the midpoint of the data range and a simple measure of central tendency.

Why is midrange sensitive to outliers?

It uses only the two extreme values. One high or low outlier changes min or max, which directly shifts the midrange.

When should I use midrange?

Rarely. Use it only for symmetric, outlier-free data when you need a quick estimate. Prefer mean or median in most cases.

What is breakdown point?

The fraction of data that can be corrupted before the statistic becomes meaningless. Midrange has 0%.

What is trimmed mean?

The mean after removing a percentage (e.g., 10%) of the smallest and largest values. More robust than the ordinary mean.

Midrange by the Numbers

0%
Breakdown Point
2
Values Used (min, max)
50%
Median Breakdown
10%
Trimmed Each Tail

Disclaimer: Midrange has 0% breakdown point. Do not use it when outliers are present. Prefer median or trimmed mean for robust analysis.

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