Range of a Data Set

Range measures the spread of a data set by finding the difference between the maximum and minimum values, telling you how dispersed your data is.

R=xmax⁡−xmin⁡R = x_{\max} - x_{\min}

Solve a problem with Range of a Data Set

Type the problem. The solver will use Range of a Data Set where Range of a Data Set is the right tool, and tell you when it is not.

Drag one in or paste from the clipboard. JPEG, PNG or WebP. You get the transcription to check before anything is solved.

How to get a better answer
  • Paste the whole problem, including the instruction word — "simplify", "solve for x" and "factor" lead to three different answers.
  • Say what you have already tried. "I got x = 4 and the book says 2" turns a solution into a diagnosis.
  • Set the level in the settings button. A calculus shortcut is not a better answer if you have not met derivatives yet.
  • For a photo, get the whole problem in frame and hold the page flat — you get the transcription to fix before anything is solved.

What each symbol means

What Range of a Data Set takes
RR
xx
Range of a Data Set →
SymbolMeaning
RRThe range—the difference between the largest and smallest values in your data set. It is always zero or positive and has the same units as your data.
xxA data value in your set; the subscripts max and min indicate the largest and smallest values respectively.

When to use it

Use range when you want to quickly see how spread out your data is, from the smallest to the largest value.

Level

Usually taught in: Pre-Algebra

Worked examples

1. Find the range of a simple data set

Problem

Find the range of this data set: 2, 5, 8, 3, 9
  1. xmax⁡=9,xmin⁡=2x_{\max} = 9, \quad x_{\min} = 2

    Identify the largest and smallest values by scanning all the numbers.

  2. R=xmax⁡−xmin⁡R = x_{\max} - x_{\min}

    Apply the range formula: subtract the minimum from the maximum.

  3. R=9−2=7R = 9 - 2 = 7

    Perform the subtraction to find the range.

Answer: R=7R = 7

The range is 7, meaning the data spreads across 7 units from smallest to largest. This shows the width of your entire data set.

2. Find the range with negative numbers and decimals

Problem

Find the range of this data set: −3,2,−8,5.5,1-3, 2, -8, 5.5, 1
  1. xmax⁡=5.5,xmin⁡=−8x_{\max} = 5.5, \quad x_{\min} = -8

    Identify the largest value (5.55.5) and the smallest value (−8-8).

  2. R=xmax⁡−xmin⁡R = x_{\max} - x_{\min}

    Set up the range formula.

  3. R=5.5−(−8)=5.5+8R = 5.5 - (-8) = 5.5 + 8

    Subtracting a negative equals adding: 5.5−(−8)=5.5+85.5 - (-8) = 5.5 + 8.

  4. R=13.5R = 13.5

    Complete the addition to find the range.

Answer: R=13.5R = 13.5

When the minimum is negative, be careful: R=5.5−(−8)R = 5.5 - (-8) becomes 5.5+8=13.55.5 + 8 = 13.5. The negative sign reverses the operation from subtraction to addition.

3. Find the range of speeds on a two-leg road trip

Problem

A family records speeds during a road trip. First leg: 45 mph, 52 mph, 48 mph. Second leg: 55 mph, 60 mph, 50 mph. What is the range of speeds for the entire trip?
  1. Data: 45,52,48,55,60,50 mph\text{Data: } 45, 52, 48, 55, 60, 50 \text{ mph}

    Combine all speeds from both legs.

  2. xmax⁡=60 mph,xmin⁡=45 mphx_{\max} = 60 \text{ mph}, \quad x_{\min} = 45 \text{ mph}

    Find the highest speed (60 mph on leg two) and lowest speed (45 mph on leg one).

  3. R=xmax⁡−xmin⁡R = x_{\max} - x_{\min}

    Apply the range formula with these values.

  4. R=60−45=15 mphR = 60 - 45 = 15 \text{ mph}

    Subtract to find the range.

Answer: R=15 mphR = 15 \text{ mph}

The range of 15 mph shows that speeds varied by 15 miles per hour across the trip, from a minimum of 45 mph to a maximum of 60 mph. This tells the family how much their speed changed between the two legs.

Common mistakes

Where Range of a Data Set usually goes wrong
Answer came out wrong
Writing R=5−(−3)=5−3=2R = 5 - (-3) = 5 - 3 = 2
Write R=5−(−3)=5+3=8R = 5 - (-3) = 5 + 3 = 8 to correctly add when subtracting a negative number.
Using the median or middle value as the range
Always calculate R=xmax⁡−xmin⁡R = x_{\max} - x_{\min}—subtract only the smallest from the largest value.
Picking the wrong maximum or minimum from unsorted data
Sort your data first (smallest to largest), then identify the first value as xmin⁡x_{\min} and the last as xmax⁡x_{\max}.
The mistakeWhy it is wrongThe fix
Writing R=5−(−3)=5−3=2R = 5 - (-3) = 5 - 3 = 2Subtracting a negative means you add instead; forgetting this reversal gives the wrong answer.Write R=5−(−3)=5+3=8R = 5 - (-3) = 5 + 3 = 8 to correctly add when subtracting a negative number.
Using the median or middle value as the rangeRange is the difference between max and min, not a single middle value; confusing it with median produces the wrong answer.Always calculate R=xmax⁡−xmin⁡R = x_{\max} - x_{\min}—subtract only the smallest from the largest value.
Picking the wrong maximum or minimum from unsorted dataWithout sorting, it is easy to miss the true largest or smallest value, which makes the range incorrect.Sort your data first (smallest to largest), then identify the first value as xmin⁡x_{\min} and the last as xmax⁡x_{\max}.

Tips and when to use something else

  • Always sort your data first to make finding the maximum and minimum easier and safer.
  • Watch out with negative numbers: subtracting a negative equals adding, so R=10−(−5)=10+5=15R = 10 - (-5) = 10 + 5 = 15.
  • Outliers (very large or very small values) make range larger because range uses only the extremes.
  • If outliers distort your data, use Interquartile Range instead, which focuses on the middle 50% of values.

Related formulas

MedianThe median is the middle value of ordered data, most useful when your data contains outliers that would skew the mean value.Arithmetic MeanArithmetic Mean is the average value found by adding all numbers in a dataset and dividing by how many numbers there are.Interquartile RangeThe interquartile range measures the spread of the middle 50% of your data, telling you how compressed or spread out typical values are.Standard DeviationStandard deviation measures how spread out data points are from the average—use it to understand variability in a dataset.

Frequently asked questions

What is the range of the data set 3, 7, 2, 9, 5?
Identify the maximum (9) and minimum (2), then calculate R=9−2=7R = 9 - 2 = 7. The range is 7.
Does range show how spread out data is?
Yes, range measures spread by showing the distance from smallest to largest value. A larger range means your data points are farther apart; a smaller range means they cluster closer together.
Why does one outlier make my range so large?
Range depends only on the maximum and minimum, so a single extreme value can inflate it dramatically. For a measure less sensitive to outliers, use Interquartile Range, which captures the middle 50% of your data.
Can the range be negative?
No, range is always zero or positive because you subtract the minimum from the maximum, and by definition the maximum is at least as large as the minimum. If all values are identical, the range is zero.

Need a different method?

The full solver is not scoped to one formula — type any problem and it will pick the method.

Open the math solver

Reviewed 2026-09-18