Descriptive Statistics
Midrange Calculator
The midrange averages the smallest and largest values, and the midhinge averages the lower and upper quartiles of the same list.
Worksheet
Press Calculate to see the result.
The midrange averages the smallest and largest values, and the midhinge averages the lower and upper quartiles of the same list.
What this calculator answers
The values 4, 9, 13, 15, and 28 have a halfway point between the extremes that is not the same as the halfway point between the quartiles. The midrange only sees 4 and 28, so 28 pulls it up. The midhinge sees Q1 and Q3, which on this list are 9 and 15, so the far 28 never enters that second average. Printing both keeps you from treating the extreme halfway mark as if it were resistant. Quartiles follow Hyndman-Fan type 7 so the midhinge matches the five-number summary page.
The headline is the midrange, (minimum + maximum) / 2. The midhinge, (Q1 + Q3) / 2, is the comparison figure from the central half. 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
Midrange and midhinge uses this relationship.
midrange = (min + max) / 2. midhinge = (Q1 + Q3) / 2.
- min. Smallest value.
- max. Largest value.
- Q1. Lower quartile, Hyndman-Fan type 7.
- Q3. Upper quartile, Hyndman-Fan type 7.
The midrange is the center of the range, so any new extreme moves it. The midhinge is the center of the quartile box, so points beyond Q1 and Q3 move it only when they change those quartiles. 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 ordered values are 4, 9, 13, 15, 28. The minimum is 4 and the maximum is 28. The midrange is (4 + 28) / 2 = 16.
Quartiles use Hyndman-Fan type 7. Q1 is 9 and Q3 is 15. The midhinge is (9 + 15) / 2 = 12.
The headline is the midrange, 16. The midhinge is the center of the quartile box, not a second midrange. Interior values affect the midhinge only by changing Q1 or Q3. They never enter the midrange unless they are an extreme.
| Midrange | 16 |
|---|---|
| Midhinge | 12 |
| Minimum | 4 |
| Maximum | 28 |
| Q1 | 9 |
| Q3 | 15 |
A second situation
28 is replaced by 4, so the upper extreme falls back to 15
The ordered values are 4, 4, 9, 13, 15. The minimum is 4 and the maximum is 15. The midrange is (4 + 15) / 2 = 9.5.
Quartiles use Hyndman-Fan type 7. Q1 is 4 and Q3 is 13. The midhinge is (4 + 13) / 2 = 8.5.
The headline is the midrange, 9.5. The midhinge is the center of the quartile box, not a second midrange. Interior values affect the midhinge only by changing Q1 or Q3. They never enter the midrange unless they are an extreme.
| Midrange | 9.5 |
|---|---|
| Midhinge | 8.5 |
| Minimum | 4 |
| Maximum | 15 |
| Q1 | 4 |
| Q3 | 13 |
Replacing 28 with 4 makes the extremes 4 and 15, so the midrange falls from 16 to 9.5. The quartiles become 4 and 13, and the midhinge falls from 12 to 8.5. 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
28 was replaced by 4, which removes the high extreme. The headline result went from 16 to 9.5.
The nudged inputs
The ordered values are 4, 4, 9, 13, 15. The minimum is 4 and the maximum is 15. The midrange is (4 + 15) / 2 = 9.5.
Quartiles use Hyndman-Fan type 7. Q1 is 4 and Q3 is 13. The midhinge is (4 + 13) / 2 = 8.5.
The headline is the midrange, 9.5. The midhinge is the center of the quartile box, not a second midrange. Interior values affect the midhinge only by changing Q1 or Q3. They never enter the midrange unless they are an extreme.
| Midrange | 9.5 |
|---|---|
| Midhinge | 8.5 |
| Minimum | 4 |
| Maximum | 15 |
| Q1 | 4 |
| Q3 | 13 |
How to read the result
A midrange of 16 is halfway from 4 to 28. It is not the mean of the five values, and the midhinge of 12 is closer to the body of the list because 28 is outside the quartiles. 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
- Minimum, maximum, and the type 7 quartiles are the landmarks you want.
- The values can be ordered.
- You are not trying to down-weight the extremes. The midrange does the opposite.
- Ties are allowed.
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 the midrange the mean of every typed value.
- Using the midrange as a robust center when a single bad extreme is likely.
- Mixing a midhinge from another quartile convention with these type 7 quartiles.
- Subtracting the extremes and calling that gap a midrange. That gap is the range.
Where a different calculator is the honest choice
Use the range calculator for the gap rather than the halfway point. Use the five-number summary when you want all five landmarks. Use the mean calculator when every value should pull. 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: Range Calculator, 5 Number Summary Calculator, Mean Calculator.
Check yourself
Values are 4, 9, 13, 15, and 28. What are the midrange and the midhinge?
The midrange is 16 and the midhinge is 12.
Using the result in a sentence
A quick center from a published minimum and maximum, and a check against the midhinge of the same batch, is the modest job of this page. Keep the count, the unit, and the assumption list beside any copy of the number that leaves this browser tab.
The midrange moves one unit for every two units a new maximum moves. It is a poor summary for salaries, house prices, or any batch with a long tail. 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 Midrange Calculator commit to?
This page uses Midrange and midhinge: midrange = (min + max) / 2. midhinge = (Q1 + Q3) / 2.. The midrange is the center of the range, so any new extreme moves it. The midhinge is the center of the quartile box, so points beyond Q1 and Q3 move it only when they change those quartiles. 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, 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 midrange is 16. A midrange of 16 is halfway from 4 to 28. It is not the mean of the five values, and the midhinge of 12 is closer to the body of the list because 28 is outside the quartiles. 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 the midrange the mean of every typed value. The midrange moves one unit for every two units a new maximum moves. It is a poor summary for salaries, house prices, or any batch with a long tail. 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 range calculator for the gap rather than the halfway point. Use the five-number summary when you want all five landmarks. Use the mean calculator when every value should pull. 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?
The midrange is 16 and the midhinge is 12. 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.