Descriptive Statistics
Average Calculator
The average is the equal share of the list, and the trim box drops one high value and one low value before that share is taken.
Worksheet
Press Calculate to see the result.
The average is the equal share of the list, and the trim box drops one high value and one low value before that share is taken.
What this calculator answers
Five commute times are 22, 18, 19, 21, and 55 minutes. The 55-minute morning is a delay, not the usual ride, and it still belongs in an untrimmed average because it happened. Ticking the trim box throws out one shortest ride and one longest ride, then averages what remains. The headline says which of those two choices was used, so a reader does not have to guess whether 55 stayed in the total. The page keeps the definition fixed while the ticket updates, so a hand check can match every intermediate term. The worksheet asks for Numbers, Trim one high and one low, and it refuses a blank that the formula cannot interpret. Treat the loaded example as a rehearsal for the live numbers you will type next, not as a claim about your own data.
With the box off, every typed number is added and divided by the count. With the box on and at least three numbers, one minimum and one maximum are removed first and the mean of the rest is the headline. Supporting counts and intermediate terms sit under the headline so a reader can see what was divided by what. When a checkbox or a tail setting changes the divisor or the rejection region, that choice appears in the steps rather than vanishing into a silent default.
The formula, written out
Arithmetic average, optionally trimmed uses this relationship.
Untrimmed: sum / n. Trimmed: sum of the list after deleting one minimum and one maximum, divided by n - 2.
- sum. Total of the values that remain in the average.
- n. How many values were typed before any trim.
- minimum. The smallest typed value. Trim removes one copy.
- maximum. The largest typed value. Trim removes one copy.
An untrimmed average gives every observation the same vote, including a delay. A one-and-one trim answers a different question: what the middle of the batch looks like after the two extremes are set aside. The algebra is the named textbook identity for this worksheet. Intermediate products and quotients appear in order so a calculator and a pencil can agree to the displayed rounding. If a neighbouring page uses a different divisor or a continuity correction, that page says so on its own ticket.
A full worked example
Example loaded in the worksheet
The form is prefilled with a small example so every arithmetic step can be checked by hand. Change one field after you finish the walkthrough and confirm the ticket moves the way the formula predicts.
The typed values are 22, 18, 19, 21, 55, and there are 5 of them. The trim box is off, so no high or low value is removed. The values that enter the average are 22, 18, 19, 21, 55.
Their sum is 135. Divide that sum by 5: 135 / 5 = 27. The headline is an untrimmed mean of 27 because trimming did not happen.
Each remaining value has an equal vote. This is not a weighted average. The unit of the result is the unit of the numbers you typed.
| Untrimmed mean | 27 |
|---|---|
| Sum used | 135 |
| Values in the average | 5 |
| Values typed | 5 |
A second situation
The trim box is on, so one low minute and one high minute drop out
The typed values are 22, 18, 19, 21, 55, and there are 5 of them. The trim box is on, so one low value of 18 and one high value of 55 are removed. The values that enter the average are 22, 19, 21.
Their sum is 62. Divide that sum by 3: 62 / 3 = 20.6667. The headline is a trimmed mean of 20.6667 because trimming happened.
Each remaining value has an equal vote. This is not a weighted average. The unit of the result is the unit of the numbers you typed.
| Trimmed mean | 20.6667 |
|---|---|
| Sum used | 62 |
| Values in the average | 3 |
| Values typed | 5 |
With the trim box on, 18 and 55 are the values removed, and 19, 21, and 22 remain. Their average is 20.6667 minutes, against an untrimmed average of 27 minutes that still contains the delay. The second example changes the feature that this formula is sensitive to, and the ticket shows the new figure beside the same definition. That contrast is the fastest way to see which input owns the movement.
What moves when the input moves
The last commute changed from 55 minutes to 80 minutes, and the trim box stayed off. The headline result went from 27 to 32.
The nudged inputs
The typed values are 22, 18, 19, 21, 80, and there are 5 of them. The trim box is off, so no high or low value is removed. The values that enter the average are 22, 18, 19, 21, 80.
Their sum is 160. Divide that sum by 5: 160 / 5 = 32. The headline is an untrimmed mean of 32 because trimming did not happen.
Each remaining value has an equal vote. This is not a weighted average. The unit of the result is the unit of the numbers you typed.
| Untrimmed mean | 32 |
|---|---|
| Sum used | 160 |
| Values in the average | 5 |
| Values typed | 5 |
How to read the result
Read the label before the number. An untrimmed mean of 27 minutes includes the 55-minute morning, while a trimmed mean of 20.6667 minutes is the typical ride with that morning set aside. Say the unit, the sample size or contract terms, and the formula name in the same sentence as the figure. A number without those three pieces invites a later reader to invent a definition that this page never used.
Write the result with its unit, the inputs that produced it, and the name of the formula. Write the result with its unit, the inputs that produced it, and the name of the formula. If the ticket shows a decision sentence, quote the alpha and the tail with it. If the ticket shows a money or dose figure, quote the rate and the schedule that produced it.
Assumptions that have to stay true
- The numbers are in one unit and can be added.
- Trimming is a choice you want, not a silent default.
- Ties lose only one copy of the extreme, not every copy.
- A missing time is left blank rather than entered as zero.
If an assumption above is false, do not average the discomfort away. Change the worksheet or change the question. A correct arithmetic step on the wrong model is still the wrong answer for the decision you are trying to make.
Mistakes that change the answer
- Calling a trimmed mean the average of the original list.
- Trimming more than one high and one low and still using this page's label.
- Averaging speeds or ratios that should have been weighted by time or distance.
- Dropping the high value by hand and also ticking the box, so it is removed twice.
Where a different calculator is the honest choice
Use the mean calculator when nothing should be removed. Use the median calculator when you want the middle rank instead of a trimmed sum. Use the arithmetic mean calculator when you also want the geometric and harmonic comparisons. Related links under the essay open pages that keep their own formulas instead of hiding a mode switch inside this ticket.
When the job changes, move to a page built for that job: Mean Calculator, Median Calculator, Arithmetic Mean Calculator.
Check yourself
Commutes take 22, 18, 19, 21, and 55 minutes, and the trim box is off. What is the average?
All five times stay in the sum of 135, so the untrimmed mean is 27 minutes.
Using the result in a sentence
Judged performances that drop a high and a low mark, and small batches with one known glitch, are the settings where this switch earns its place. Keep the count, the unit, and the assumption list beside any copy of the number that leaves this browser tab.
Trimming one high and one low does not fix a list that is skewed in only one direction. It also discards real events. Say so if the 55-minute morning is the delay you are trying to manage. Pair the headline with the steps before you staff a route, set a grade boundary, or compare two contracts from a single number.
Questions people ask next
01What definition does the Average Calculator commit to?
This page uses Arithmetic average, optionally trimmed: Untrimmed: sum / n. Trimmed: sum of the list after deleting one minimum and one maximum, divided by n - 2.. An untrimmed average gives every observation the same vote, including a delay. A one-and-one trim answers a different question: what the middle of the batch looks like after the two extremes are set aside. If a textbook uses a different divisor, a different continuity correction, or a different rounding rule, the last digits can move, so the definition is printed above the result. The worksheet asks for Numbers, Trim one high and one low, and it refuses a blank that the formula cannot interpret. Keep that printed definition in the sentence you write next to the figure so a later reader can rebuild the arithmetic without guessing which convention you chose.
02How should the worked example be read out loud?
In the loaded example the untrimmed mean is 27. Read the label before the number. An untrimmed mean of 27 minutes includes the 55-minute morning, while a trimmed mean of 20.6667 minutes is the typical ride with that morning set aside. Say the unit and the count before you say whether the number is large or small. Read the steps in order rather than jumping to the headline, because the intermediate terms are where a swapped percent and proportion usually hide. If the ticket shows both a primary figure and a comparison figure, name which one you are quoting.
03What is the fastest way to get a misleading result?
Calling a trimmed mean the average of the original list. Trimming one high and one low does not fix a list that is skewed in only one direction. It also discards real events. Say so if the 55-minute morning is the delay you are trying to manage. A second common failure is leaving a checkbox or tail setting in the wrong state and then treating the number as if the default had matched your plan. Reset the example, change one input, and confirm the ticket moves in the direction the formula predicts before you trust a live run.
04When should I leave this page for a different calculator?
Use the mean calculator when nothing should be removed. Use the median calculator when you want the middle rank instead of a trimmed sum. Use the arithmetic mean calculator when you also want the geometric and harmonic comparisons. The related links under the essay go to those worksheets, which keep their own formulas instead of hiding them in a mode switch. If the question changed from a summary to a test, from a payment to a refinance, or from a raw score to a percentile, switch pages rather than forcing this ticket to answer a job it was not built for.
05What belongs in the sentence next to the number?
All five times stay in the sum of 135, so the untrimmed mean is 27 minutes. Name the formula, the sample size or the inputs, and the unit before you compare the figure with someone else's. A bare number without those three pieces cannot be audited when a score, a rate, or a lab value is challenged later. Store the inputs beside the result whenever the figure will travel into a report.