Quartile and IQR Calculator
Paste a data set to get the quartiles, interquartile range, five number summary and outliers, with a box plot and the working for your chosen method.
- Q1, Q2, Q3 & IQR
- Five number summary
- Outliers (1.5 × IQR)
- Box plot
Your data
11 values.
Results
Q1 (lower quartile)
15
Median (Q2)
40
Q3 (upper quartile)
43
Interquartile range (IQR)
28
Center
- Count (n)
- 11
- Sum (Σx)
- 365
- Mean
- 33.1818
- Median
- 40
- Mode
- No mode
Spread
- Sample standard deviation (s)
- 15.8734
- Population standard deviation (σ)
- 15.1347
- Sample variance (s²)
- 251.9636
- Population variance (σ²)
- 229.0579
- Sum of squares (SS)
- 2,519.6364
- Mean absolute deviation
- 13.0083
- Standard error of the mean
- 4.786
- Coefficient of variation (s ÷ mean)
- 47.84%
- Minimum
- 6
- Maximum
- 49
- Range
- 43
Quartiles and outliers
- Q1
- 15
- Q3
- 43
- Interquartile range (IQR)
- 28
- Five number summary
- 6, 15, 40, 43, 49
- Outlier fences
- −27 and 85
- Outliers (1.5 × IQR)
- None
Empirical rule (using s)
- Within 1 SD (68% if normal)
- 8 of 11 (72.7%)
- Within 2 SD (95% if normal)
- 11 of 11 (100%)
- Within 3 SD (99.7% if normal)
- 11 of 11 (100%)
Step-by-step working
Sort the data from smallest to largest
6, 7, 15, 36, 39, 40, 41, 42, 43, 47, 49
Find the median (Q2)
Middle value of the sorted list
With n = 11, the median is the 6th value: 40.
Find Q1, the median of the lower half
Lower half: first 5 values
The median is left out of both halves (the method used by TI-84 calculators and most textbooks).
Lower half: 6, 7, 15, 36, 39
Q1 = 15
Find Q3, the median of the upper half
Upper half: last 5 values
Upper half: 41, 42, 43, 47, 49
Q3 = 43
Subtract to get the interquartile range
IQR = Q3 − Q1
IQR = 43 − 15 = 28
Check for outliers with the 1.5 × IQR rule
Fences = Q1 − 1.5 × IQR and Q3 + 1.5 × IQR
Lower fence = 15 − 1.5 × 28 = −27
Upper fence = 43 + 1.5 × 28 = 85
No value falls outside the fences, so there are no outliers.
| # | x | x − x̄ | (x − x̄)² | z |
|---|---|---|---|---|
| 1 | 6 | −27.1818 | 738.8512 | −1.7124 |
| 2 | 7 | −26.1818 | 685.4876 | −1.6494 |
| 3 | 15 | −18.1818 | 330.5785 | −1.1454 |
| 4 | 36 | 2.8182 | 7.9421 | 0.1775 |
| 5 | 39 | 5.8182 | 33.8512 | 0.3665 |
| 6 | 40 | 6.8182 | 46.4876 | 0.4295 |
| 7 | 41 | 7.8182 | 61.124 | 0.4925 |
| 8 | 42 | 8.8182 | 77.7603 | 0.5555 |
| 9 | 43 | 9.8182 | 96.3967 | 0.6185 |
| 10 | 47 | 13.8182 | 190.9421 | 0.8705 |
| 11 | 49 | 15.8182 | 250.2149 | 0.9965 |
| Σ | 365 | 0 | 2,519.6364 |
Rows with |z| above 3 are highlighted. The Σ row of x shows Σx.
What are quartiles and the interquartile range?
Quartiles split sorted data into four equal parts. Q1, the lower quartile, has a quarter of the values below it; Q2 is the median; Q3, the upper quartile, has three quarters below it. The interquartile range (IQR = Q3 − Q1) is the spread of the middle half of the data, and unlike the range or standard deviation it is not pulled around by extreme values. Together with the minimum and maximum, the quartiles form the five number summary that a box plot draws. Values more than 1.5 × IQR below Q1 or above Q3 are flagged as outliers. One catch: there are several accepted ways to compute quartiles, and textbooks, TI calculators and Excel do not always agree. This calculator lets you pick the method and shows exactly how each quartile was found.
How to find quartiles and the IQR
- Type or paste your data. It does not need to be sorted.
- Pick the quartile method: Textbook / TI-84 (median of each half), Excel QUARTILE.INC, or Excel QUARTILE.EXC.
- Read Q1, the median, Q3, the IQR and the five number summary, and check the box plot.
- See which values are outliers and how the fences were calculated in the step-by-step working.
Quartile and IQR formulas
- Interquartile range
IQR = Q3 − Q1
Spread of the middle half of the data.
- Outlier fences
Q1 − 1.5 × IQR and Q3 + 1.5 × IQR
Values outside the fences are flagged as outliers.
- Excel QUARTILE.INC position
position = (n − 1) × p + 1
p = 0.25 for Q1 and 0.75 for Q3; interpolate between neighbours.
- Excel QUARTILE.EXC position
position = (n + 1) × p
The (n + 1)p rule, also used by Minitab and SPSS.
Why use this quartile calculator
- Three methods, clearly labelledSwitch between the textbook / TI-84 method and Excel’s QUARTILE.INC and QUARTILE.EXC to match your class or spreadsheet, and see why the answers differ.
- Box plot and outliersThe five number summary is drawn as a box plot under a histogram, and outliers beyond the 1.5 × IQR fences are listed.
- Working shown with your numbersEvery answer comes with the formula and each line of arithmetic filled in with your data, plus a table of deviations, so you can check homework or copy the method into an exam answer.
- Paste straight from a spreadsheetCopy a column from Excel, Google Sheets or Numbers and paste it. Commas, spaces, tabs and new lines all work, headers like “Score” are skipped, and multi-column pastes let you pick one column.
- Every summary statistic at onceMean, median, mode, range, quartiles, IQR, outliers, standard error, coefficient of variation, mean absolute deviation and z-scores for each value appear together.
- Private, free and instantCalculations run in your browser as you type. Nothing is sent to a server, there is no sign-up, no limit on how many numbers you enter and no “show steps” paywall.
Common uses for quartiles and the IQR
- Statistics homework. Check answers for AP Statistics, intro stats and lab reports, and copy the step-by-step working.
- Box plots. Get the five numbers you need to draw a box-and-whisker plot by hand or in a report.
- Outlier checks. Find suspicious values before averaging data.
- Salaries and prices. Describe skewed data such as incomes or house prices, where the IQR is more honest than the standard deviation.
- Grades and test scores. See how spread out a class’s scores are and how far one score sits from the average.
- Surveys and research. Describe survey responses or experimental groups before running a t-test or building a confidence interval.
The same statistics in Excel, Google Sheets and a TI-84
To check an answer or redo it in a spreadsheet, use these functions (they work the same in Google Sheets). On a TI-83 or TI-84, enter the data in L1, press STAT, CALC, 1-Var Stats; for a frequency table put the counts in L2 and set FreqList to L2.
| Statistic | Excel and Google Sheets | TI-84 (1-Var Stats) |
|---|---|---|
| Sample standard deviation (s) | =STDEV.S(A2:A20) | Sx |
| Population standard deviation (σ) | =STDEV.P(A2:A20) | σx |
| Sample variance (s²) | =VAR.S(A2:A20) | Sx² |
| Population variance (σ²) | =VAR.P(A2:A20) | σx² |
| Mean | =AVERAGE(A2:A20) | x̄ |
| Median | =MEDIAN(A2:A20) | Med |
| Mode | =MODE.MULT(A2:A20) | Not shown |
| Q1 and Q3 | =QUARTILE.INC(A2:A20, 1) and 3, or QUARTILE.EXC | Q1, Q3 (textbook method) |
| Sum of squares (SS) | =DEVSQ(A2:A20) | Not shown (Σx² is) |
| Mean absolute deviation | =AVEDEV(A2:A20) | Not shown |
| Standard error of the mean | =STDEV.S(A2:A20)/SQRT(COUNT(A2:A20)) | Sx ÷ √n |
| Z-score of a value | =STANDARDIZE(x, mean, sd) | (x − x̄) ÷ Sx |
| Percentile from a z-score | =NORM.S.DIST(z, TRUE) | normalcdf(−1E99, z) |
What this calculator does that most others leave out
We compared the top standard deviation, variance, z-score and quartile calculators in October 2026. Most return one number for one mode, show the formula without your numbers, or cap the number of values. This one was built to cover the gaps.
- Both versions at once. Most calculators make you pick sample or population first. Here s, σ, s² and σ² are always on screen.
- Working with your own numbers. Not just the formula: the mean, every squared deviation, the sum of squares and the final square root are written out with your data.
- Frequency and grouped data. Enter value and count pairs or class intervals instead of typing repeated numbers.
- Quartiles that match your class. Choose the textbook / TI-84 method or Excel’s QUARTILE.INC or QUARTILE.EXC.
- Z-scores and outliers. Every value gets a z-score, and values beyond 1.5 × IQR or 3 standard deviations are flagged.
- No limits, fully private. Paste thousands of values or open a CSV file. Everything is processed on your device and never sent anywhere.
More math and statistics tools
Only need the mean, median and mode, or a weighted average for grades? Use the average calculator. For percentages and percent change, try the percentage calculator, and to type formulas like σ = √(Σ(x − μ)² ÷ N) for a report, use the online math editor. Browse all student tools and calculators.
Worked example: quartiles of 11 values
Data (sorted): 6, 7, 15, 36, 39, 40, 41, 42, 43, 47, 49. Median: the 6th value, 40. Textbook / TI-84 method: lower half 6, 7, 15, 36, 39 gives Q1 = 15; upper half 41, 42, 43, 47, 49 gives Q3 = 43; IQR = 28. Excel QUARTILE.INC gives Q1 = 25.5 and Q3 = 42.5 (IQR 17), and QUARTILE.EXC gives 15 and 43. Fences (textbook): 15 − 1.5 × 28 = −27 and 43 + 1.5 × 28 = 85, so there are no outliers. Five number summary: 6, 15, 40, 43, 49.
What to expect from the result
Different methods can give different quartiles for the same data, especially for small data sets; choose the one your class or software uses. Excel’s QUARTILE.EXC is undefined for very small data sets (fewer than 3 values for Q1 and Q3). The 1.5 × IQR rule is a convention for flagging possible outliers, not proof that a value is wrong.
Quartile and IQR Calculator questions
How do you find Q1 and Q3?
Sort the data and find the median. Q1 is the median of the lower half and Q3 the median of the upper half. If the number of values is odd, the textbook and TI-84 method leaves the median out of both halves.
Why are my quartiles different from Excel?
Excel’s QUARTILE and QUARTILE.INC interpolate between values using position (n − 1) × p + 1, while most textbooks and TI calculators take the median of each half. Both are valid. Switch the method here to match the one you need.
How do you calculate the IQR?
Subtract the first quartile from the third: IQR = Q3 − Q1. It covers the middle 50% of the data.
How do you find outliers with the IQR?
Compute the lower fence Q1 − 1.5 × IQR and the upper fence Q3 + 1.5 × IQR. Any value below the lower fence or above the upper fence is an outlier. Some courses also use 3 × IQR for extreme outliers.
What is the five number summary?
Minimum, Q1, median, Q3 and maximum. It describes the centre, spread and range of the data and is exactly what a box-and-whisker plot shows.