FTM

Math & Statistics

Five-Value Trimmed Mean Calculator

Calculate the five-value total, one removed minimum, one removed maximum, three-value trimmed sum and mean, ordinary mean, trimming effect, and comparison gap. Review the complete derivation, duplicate-extreme handling, interpretation, and limitations.

Value 1Value 2Value 3Value 4Value 5Entered comparison

Three-value trimmed mean-

Sum of all five values-

Minimum value removed-

Maximum value removed-

Sum after removing one minimum and maximum-

Ordinary five-value mean-

Trimmed minus ordinary mean-

Trimmed mean minus comparison-

Decision view

Sorted observations and the removed extremes

Sorted observations and the removed extremesA ranked dot plot crosses out one minimum and maximum, highlights the retained center, and compares both means.

Exact scenario comparisonValue 5 changes while all other entered assumptions remain constant.

Value 5	Three-value trimmed mean	Sum of all five values	Minimum value removed	Maximum value removed	Sum after removing one minimum and maximum	Ordinary five-value mean	Trimmed minus ordinary mean	Trimmed mean minus comparison

How to use Five-Value Trimmed Mean Calculator

Enter five observations measured on the same scale.
Inspect which single minimum and maximum are removed.
Compare the trimmed mean with the ordinary mean and the original range.
Report the trimming rule because removing 40% of a five-value sample is substantial.

Calculator guide

Understanding Five-Value Trimmed Mean Calculator

This five-value trimmed mean removes exactly one minimum and one maximum, then averages the remaining three observations. The page shows the removed contribution and ordinary mean so the effect of trimming cannot be hidden.

Rule is exact One minimum and one maximum are removed.

Duplicates remain separate Only one occurrence at each selected extreme is trimmed.

Forty percent is removed The small sample makes trimming aggressive.

Show both means The comparison exposes the influence of extremes.

Calculation method

How the calculation works

Remove exactly one minimum and one maximum from five entered values and average the remaining three while reconciling the removed contribution. In the Five-Value Trimmed Mean Calculator, the live scenario varies value 5 and tracks three-value trimmed mean while the remaining results preserve the reconciliation path. Add all five values, identify one minimum and one maximum, subtract those two observations from the total, and divide the remaining sum by three. The ordinary mean divides the original total by five, and the trimming effect subtracts ordinary mean from trimmed mean.

Detailed calculation process

Remove the two extremes and reconcile the mean

The default example makes the high value's influence visible by showing the original sum, removed values, and remaining three observations.

General formula: TM = [sum from i=1 to 5 of x_i - min(x) - max(x)] / (5 - 2) Add all five values, remove exactly one lowest and one highest observation, and divide the remaining total by the three observations left.

What each symbol means

TM Trimmed mean after removing one observation from each tail.

x_i The observation at position i.

min(x) One occurrence of the smallest entered value.

max(x) One occurrence of the largest entered value.

5 - 2 Five original observations minus the two removed extremes.

Worked substitution with the default inputs

1. Add all observations: 18 + 21 + 20 + 19 + 52 = 130 The original total is the starting point for both ordinary and trimmed means.

2. Identify one minimum and maximum: minimum = 18; maximum = 52 Exactly one observation at each extreme is removed, even when an extreme value is duplicated.

3. Form the trimmed sum: 130 - 18 - 52 = 60 The remaining values are 19, 20, and 21.

4. Calculate both means: trimmed mean = 60 / 3 = 20; ordinary mean = 130 / 5 = 26 Both results trace back to the same original five observations.

5. Measure the trimming effect: 20 - 26 = -6; 20 - comparison 20 = 0 Trimming lowers the mean by six units and matches the entered comparison in the default scenario.

Removing 18 and 52 leaves a sum of 60 across 19, 20, and 21, so the trimmed mean is 20 instead of the ordinary mean of 26.

Robust-summary check

What the trim changes and what it cannot decide

Trimming controls influence but does not explain why an extreme exists.

Influence Extreme magnitudes no longer enter the three-value average.

Rank Selection depends on order, not distance from center.

Validity A trimmed observation may still be correct and meaningful.

Reporting Keep the original observations and rule available.

Worked situations

Practical examples

The value 52 raises the ordinary mean to 26 while the trimmed mean remains 20.
If the minimum occurs twice, only one copy is removed and the other remains in the three-value center.
When values are symmetric, trimming can leave the mean unchanged.

Better inputs

Useful tips

Review extreme observations for context rather than assuming they are errors.
Use the same predetermined trimming rule across comparisons.
Retain the ordinary mean and full data when reporting the trimmed result.

Before relying on the result

Limitations and common mistakes

Removing two of five observations discards 40% of the sample.
The method does not determine whether an extreme is an error, a valid rare case, or an important signal.
A five-value trimmed mean is not a substitute for an analysis of sampling, distribution, or measurement quality.

Reference

Key terms

Trimmed mean: Mean after removing a stated number or percentage of observations from both tails.
Trimmed sum: Original total after subtracting one minimum and one maximum.
Ordinary mean: Original five-value total divided by five.
Trimming effect: Trimmed mean minus ordinary mean.

Important note

Calculated directly from the entered values using the displayed formula and rounding settings.

Frequently asked questions

What if the minimum or maximum appears more than once?

Only one occurrence of each selected extreme is removed; duplicate observations are distinct entries.

Is the highest value automatically an outlier?

No. The calculator trims by rank and does not perform an outlier test.

Why divide by three?

Five original observations minus one minimum and one maximum leaves three observations.

Can I use this for larger datasets?

This page is fixed to five values and one observation per tail; larger datasets need an explicitly chosen trimming percentage and algorithm.