What Is Midrange? (Quick Answer)
To find the midrange, identify the smallest and largest values in the data set, add them together, and divide by 2. Formula: Midrange = (Minimum + Maximum) / 2. Example: for 4, 7, 10, 13, 18 — minimum is 4 and maximum is 18, so the midrange is (4 + 18) / 2 = 11.
The midrange belongs to the same family as the mean, median, and mode — it gives you a number that describes the center of a data set. What sets it apart is its simplicity: only two observations matter, the minimum and the maximum. Every value in between has no direct effect on the result.
That simplicity is both the midrange's strength and its main limitation. Quick to calculate, yes — but because one unusually large or small observation can pull the endpoints, the midrange can land far from where most of the data actually sits. A closer look at the formula, examples, and comparisons below makes that trade-off concrete.
Midrange Formula
MR = midrange
xmin = smallest value in the data set
xmax = largest value in the data set
The parentheses matter here. Writing min + max / 2 without parentheses would divide only the maximum by 2 under standard order of operations, which gives the wrong answer. Always add first, then divide: (min + max) / 2.
Wrong: (Max − Min) / 2 — this gives you half the range, not the midrange. Correct: (Max + Min) / 2 — addition, not subtraction. For Min = 4, Max = 18: wrong answer = (18 − 4)/2 = 7 | correct answer = (18 + 4)/2 = 11.
How to Find Midrange in 3 Steps
Find the Minimum Value
Scan the data set and identify the smallest number. You do not need to sort the entire list — just locate the lowest observation. For 17, 5, 12, 28, 9, 20 — the minimum is 5.
Find the Maximum Value
Identify the largest number in the data set. For 17, 5, 12, 28, 9, 20 — the maximum is 28.
Add Them and Divide by 2
Apply the formula: (Minimum + Maximum) / 2. For our example: (5 + 28) / 2 = 33 / 2 = 16.5. The midrange is 16.5, which does not appear anywhere in the original list — and that is perfectly valid.
Number Line — Midrange as the Midpoint of Endpoints
Midrange Examples — Step by Step
Basic Example With Integers
Data set: 4, 7, 10, 13, 18
Minimum: 4
Maximum: 18
Midrange: (4 + 18) / 2 = 22 / 2 = 11
✅ Midrange = 11. Note: 10 and 13 and 7 have no effect on this result once the endpoints (4 and 18) are known.
Example With Unsorted Data
You do not need to sort the data to find the midrange. Sorting may make the minimum and maximum easier to spot visually, but it is not part of the calculation.
Data set: 17, 5, 12, 28, 9, 20
Minimum: 5 (scan for smallest — no sorting required)
Maximum: 28
Midrange: (5 + 28) / 2 = 33 / 2 = 16.5
✅ Midrange = 16.5. The midrange does not appear anywhere in the original list — that is perfectly valid and expected.
Example With Decimal Values
Data set: 11.8, 13.2, 14.6, 15.3
Minimum: 11.8
Maximum: 15.3
Midrange: (11.8 + 15.3) / 2 = 27.1 / 2 = 13.55
✅ Midrange = 13.55. Decimal results are common and correct — the midrange carries the same units as the original data (e.g., centimetres, kilograms, degrees).
Example With Negative Numbers
Data set: −12, −5, 0, 4, 8
Minimum: −12 (the most negative value is the smallest)
Maximum: 8
Midrange: (−12 + 8) / 2 = −4 / 2 = −2
✅ Midrange = −2. A negative midrange is valid whenever the minimum and maximum sum to a negative number.
A common mistake: treating −12 as if it were positive when summing. Always keep the sign. For −12 and +8: (−12) + 8 = −4, not +20. Dividing −4 by 2 gives −2, not +2 or +10.
Midrange vs Range
These two statistics use the same two inputs — the minimum and maximum — but they answer different questions. The range subtracts the endpoints to measure how spread out the data is. The midrange averages them to find a central location.
Range
Measures the spread between the two extremes. It answers: how wide is the data?
Range = Max − Min
Midrange
Measures the location halfway between the two extremes. It answers: where is the center of the endpoints?
Midrange = (Max + Min) / 2
| Statistic | Formula | What It Describes |
|---|---|---|
| Range | Max − Min | Spread between the two endpoints |
| Midrange | (Max + Min) / 2 | Midpoint between the two endpoints |
Data set: 3, 6, 8, 11, 15
Minimum: 3 | Maximum: 15
Range: 15 − 3 = 12 (spread)
Midrange: (15 + 3) / 2 = 18 / 2 = 9 (center of endpoints)
✅ Range = 12 (how spread out the data is). Midrange = 9 (the midpoint between 3 and 15). They measure different things.
If you know both the midrange (m) and the range (r), you can recover the original endpoints without seeing the raw data:
For midrange = 20 and range = 12: Minimum = 20 − 6 = 14, Maximum = 20 + 6 = 26. Check: (14 + 26) / 2 = 20 ✓ and 26 − 14 = 12 ✓.
Mean, Median, Mode, and Midrange Compared
All four are measures of central location. The data set 2, 3, 3, 7, 10 shows clearly how different they can be.
Data set: 2, 3, 3, 7, 10
Mean: (2 + 3 + 3 + 7 + 10) / 5 = 25 / 5 = 5 — uses every value
Median: ordered list is 2, 3, 3, 7, 10 → middle value = 3 — uses the ordered center
Mode: 3 — appears twice, more than any other value
Midrange: (2 + 10) / 2 = 12 / 2 = 6 — uses only minimum (2) and maximum (10)
| Measure | Inputs Used | Result for 2, 3, 3, 7, 10 |
|---|---|---|
| Mean | Every value | 5 |
| Median | Ordered middle observation | 3 |
| Mode | Most frequent value | 3 |
| Midrange | Minimum + Maximum only | 6 |
Midrange vs Median — Not the Same Thing
A persistent misconception is that midrange and median are interchangeable. They are not. The median is the middle value when observations are ordered from smallest to largest. The midrange uses only the two endpoints, ignoring everything in between.
Data set: 2, 3, 4, 5, 100
Midrange: (2 + 100) / 2 = 102 / 2 = 51
Median: ordered list is 2, 3, 4, 5, 100 → middle value = 4
✅ Midrange = 51 vs Median = 4. The extreme value of 100 drags the midrange to 51, while the median stays anchored at 4, which is far closer to where most observations actually are.
Why Midrange Is Sensitive to Outliers
Because the midrange depends entirely on the two most extreme values, one unusual observation can shift it substantially. This is worth understanding before deciding whether midrange is the right tool for your data.
Before and after a single extreme observation
Dataset A: 2, 4, 5, 6, 8 → Midrange = (2 + 8) / 2 = 5 | Median = 5
Dataset B: 2, 4, 5, 6, 100 (one outlier replaces 8 with 100) → Midrange = (2 + 100) / 2 = 51 | Median = 5
✅ The midrange jumped from 5 to 51 — a change of 46 — because a single endpoint changed. The median held steady at 5 throughout. This is why the median is considered a more robust measure of center for skewed data.
Never describe the midrange as resistant to extreme values. The opposite is true. Its exclusive dependence on the minimum and maximum makes it the most sensitive of the four common measures of center to a single unusual observation.
Same Midrange, Very Different Data
Two data sets can have identical midranges while looking nothing alike. This is a concrete reminder that the midrange alone does not tell you where most observations are concentrated.
| Data Set | Values | Min | Max | Midrange | Mean |
|---|---|---|---|---|---|
| A | 0, 4, 5, 6, 10 | 0 | 10 | 5 | 5 |
| B | 0, 1, 1, 1, 10 | 0 | 10 | 5 | 2.6 |
Dataset A has a reasonably symmetric spread. Dataset B has three observations clustered near zero and one extreme outlier at 10. Their midranges are identical (both 5), but the data distributions are completely different. The midrange gives no clue about that difference.
When Midrange Is Useful (and When It Isn't)
Midrange Can Be Useful When
• Only the minimum and maximum are available
• Teaching the concept of measures of center
• Summarizing a bounded or controlled range
• Providing a quick rough center during data exploration
• Specific domain conventions require the endpoint midpoint
Exercise Caution When
• Outliers or extreme values are present
• The data distribution is skewed
• The two endpoints are unreliable or error-prone
• You need to represent a typical observation accurately
• All values in the data should contribute to the center estimate
How to Find Midrange From a Frequency Table
How you handle a frequency table depends on whether it lists exact values or grouped intervals.
Exact-Value Frequency Table
When a frequency table lists individual observed values (not intervals), finding the midrange is no different from working with raw data. Frequencies have no effect on the minimum or maximum, so they do not change the midrange calculation.
| Value | Frequency |
|---|---|
| 2 | 3 |
| 5 | 4 |
| 9 | 2 |
| 12 | 1 |
Minimum observed value: 2. Maximum: 12. Midrange: (2 + 12) / 2 = 7. The frequency column plays no role in this calculation.
Grouped Frequency Distribution — A Limitation
When a table shows grouped class intervals, the exact raw minimum and maximum are generally unknown. For example, a class labelled "0–9" might contain observations anywhere from 0 to 9. Without knowing the individual data points, you cannot determine the true midrange.
If only class intervals are available, using the lower boundary of the first class and the upper boundary of the last class gives an approximation of an interval midpoint — not the true sample midrange. Always label any such result as an approximation and clarify what was assumed.
Class Midpoint vs Data-Set Midrange
These are two different things that get confused regularly. A class midpoint (also called a class mark) is the center of a single interval: (lower limit + upper limit) / 2. This is a per-interval calculation. The data-set midrange is the midpoint between the overall minimum and maximum across the entire data set. Read assignment wording carefully — they ask for different things.
How to Find Midrange in Excel
There is no dedicated MIDRANGE function in Excel, but the formula translates directly into two built-in functions.
MIN(A2:A20) returns the smallest value
MAX(A2:A20) returns the largest value
Adjust A2:A20 to match your actual data range
This mirrors the statistical formula exactly: add the minimum and maximum, then divide by 2. An alternative that reaches the same result:
=AVERAGE(MIN(A2:A20),MAX(A2:A20)) — averages the minimum and maximum values directly. Both formulas return the same result; the first version is generally clearer because it mirrors the written formula step by step.
Excel's MIN and MAX functions ignore blank cells automatically. Text cells in the range may cause unexpected behaviour, so check that your data column contains only numeric values before running the formula.
Common Midrange Mistakes
| Mistake | Wrong Approach | Correct Approach |
|---|---|---|
| Using subtraction instead of addition | (Max − Min) / 2 = 7 for Min=4, Max=18 | (Max + Min) / 2 = 11 for Min=4, Max=18 |
| Forgetting parentheses | Min + Max / 2 (divides only Max) | (Min + Max) / 2 (adds first, then divides) |
| Confusing midrange with median | Sorting and picking the middle value | Finding Min and Max, then averaging them |
| Confusing midrange with mean | Sum of all values ÷ n | (Min + Max) / 2 — only two values involved |
| Ignoring negative signs | Min=−10, Max=4 → (10+4)/2 = 7 | (−10 + 4) / 2 = −6 / 2 = −3 |
| Thinking midrange must be in the data | Rejecting 5.5 for data 2, 4, 9 | (2 + 9) / 2 = 5.5 is correct — observed or not |
| Claiming midrange is robust | "Midrange is resistant to outliers" | Midrange is highly sensitive — one extreme endpoint changes it dramatically |
| Using class limits as exact endpoints | Taking first class lower limit as Min in grouped data | Label as approximation; grouped data hides true raw endpoints |
Midrange Calculator
Find the Midrange of Your Data
Frequently Asked Questions
Find the smallest value (minimum) and the largest value (maximum), then apply the formula: Midrange = (Minimum + Maximum) / 2. For the data set 5, 9, 14, 22: minimum is 5, maximum is 22, so midrange = (5 + 22) / 2 = 13.5.
Range = Max − Min. It measures spread — how wide the data is. Midrange = (Max + Min) / 2. It measures the midpoint location between the two extremes. For Min = 3, Max = 15: Range = 12 (spread), Midrange = 9 (location).
No. The median is the middle observation when the data is sorted. The midrange uses only the minimum and maximum. For 2, 3, 4, 5, 100 — median = 4, midrange = (2 + 100)/2 = 51. With a skewed data set or outlier, they can differ enormously.
No. The midrange uses only two values: the minimum and the maximum. Every observation between them has no direct effect on the result. This is what makes it quick to calculate but also highly sensitive to extreme endpoints.
Yes, on both counts. The midrange does not need to be a whole number or an observed value. For Min = 3, Max = 8: midrange = 5.5. For Min = −10, Max = 4: midrange = −3. Both are perfectly valid results.
No. Sorting can make the minimum and maximum easier to identify visually, but the formula only needs those two values. Sorting the entire data set is not a required step and does not change the answer.
A single outlier that becomes the new minimum or maximum can shift the midrange dramatically. For 2, 4, 5, 6, 8 — midrange = 5. Change the maximum from 8 to 100: midrange jumps to 51. The midrange is not robust to outliers.
The midrange is a measure of central location — it gives you a number that represents the center between the two endpoints. The range, by contrast, is a measure of spread. The two statistics are related but serve different purposes.
If your data are in cells A2:A20, enter this formula in an empty cell: =(MIN(A2:A20)+MAX(A2:A20))/2. Adjust the range to match your actual data. There is no dedicated MIDRANGE function in Excel, but MIN and MAX together replicate the formula exactly.
For the data set 2, 3, 3, 7, 10 — Mean = (2+3+3+7+10)/5 = 5 (all values). Median = 3 (middle after sorting). Mode = 3 (appears most often). Midrange = (2+10)/2 = 6 (average of min and max only). Each uses a different part of the data.
Practice Problems
Click Show Answer on each card to reveal the full worked solution.
Key Takeaways
- Formula: Midrange = (Minimum + Maximum) / 2 — addition, not subtraction
- Three steps: Find Min → Find Max → Add and divide by 2
- Sorting is not required — only the two endpoints matter
- The midrange does not need to be an observed value — decimal results are valid
- Range ≠ Midrange: Range = Max − Min (spread). Midrange = (Max + Min) / 2 (location)
- Midrange ≠ Median: Median uses the ordered middle observation; midrange uses only the endpoints
- Outlier sensitivity: One extreme value can shift the midrange dramatically — it is not a robust statistic
- Excel formula: =(MIN(A2:A20)+MAX(A2:A20))/2
- Grouped frequency tables: May not reveal the true raw endpoints — the exact midrange may be unknowable
- Same midrange ≠ same data: Two very different data sets can share a midrange, so it does not fully describe a distribution