Quartile Calculator (Five-Number Summary & Box Plot)

By TI 84 Calc PRO Editorial TeamLast updated

This free quartile calculator finds the five-number summary of any data set — minimum, Q1, median, Q3 and maximum — then the interquartile range (IQR), the range, and outliers by the 1.5 × IQR and 3 × IQR fence rules. It draws a box-and-whisker plot (modified, to show outliers, or regular), lets you switch between the TI-84 method (median of halves, exclusive), the inclusive method, Excel’s QUARTILE.INC and Tukey’s hinges, and includes a percentile calculator (percentile of a value, or the value at a percentile). Results update as you type, with step-by-step working and the exact TI-84 keystrokes for 1-Var Stats and STAT PLOT.

Contents

How to Use the Quartile Calculator

  1. Enter your data. Type or paste numbers separated by commas, spaces, tabs or new lines. You can paste a column straight from Excel or Google Sheets. Use the Value + frequency tab for a frequency table (for example 3, 5 means the value 3 appears 5 times).
  2. Pick a quartile method. Leave TI-84 (median of halves, exclusive) selected if you want to match 1-Var Stats on a TI-84, TI-84 Plus CE or TI-83. Switch to Inclusive, Excel QUARTILE.INC or Tukey if your teacher or spreadsheet uses one of those.
  3. Read the five-number summary in the purple boxes, then the IQR, range and any outliers. The box plot underneath is a modified box plot by default (whiskers stop at the last non-outlier, like the TI-84’s modified STAT PLOT). Choose Regular (min to max) if you want whiskers all the way to the ends.
  4. Use the percentile calculator to find the percentile of a value, or the value at a percentile (for example the 90th).
  5. Open the extras: step-by-step working with your numbers, a table of all four methods side by side, and the TI-84 keys for 1-Var Stats and STAT PLOT.

Results update as you type. Copy share link saves your inputs in the URL. Need the mean and standard deviation of the same list as well? Use the standard deviation calculator — it also lists Q1 and Q3 (TI-84 method only) alongside s and σ, without a box plot or a method choice.

What Is the Five-Number Summary?

The five-number summary is a compact picture of a data set’s centre, spread and extremes:

  • Minimum — the smallest value.
  • Q1 (first quartile, 25th percentile) — about a quarter of the values lie at or below this point.
  • Median (Q2, 50th percentile) — the middle value once the data are sorted. Half the values are at or below it.
  • Q3 (third quartile, 75th percentile) — about three quarters of the values lie at or below this point.
  • Maximum — the largest value.

From those five numbers you also get:

IQR = Q3 − Q1  Range = max − min  Midhinge = (Q1 + Q3) / 2

The IQR measures the spread of the middle half of the data and is much less sensitive to a single extreme value than the range or the standard deviation. That is why it is the usual scale for flagging outliers and for drawing a box plot.

Quartile Methods: TI-84, Inclusive, Excel and Tukey

There is no single official rule for Q1 and Q3, which is why the same list can give slightly different quartiles in a textbook, on a TI-84 and in Excel. This calculator implements the four methods students actually meet:

  • TI-84 (median of halves, exclusive) — also called the Moore and McCabe method. Sort the data, find the median, then take the median of the lower half and the median of the upper half. When n is odd the overall median is left out of both halves. This is what 1-Var Stats reports as Q1 and Q3 on a TI-84, TI-84 Plus CE or TI-83.
  • Inclusive (median of halves) — the same idea, except when n is odd the overall median is kept in both halves.
  • Excel QUARTILE.INC — Excel’s QUARTILE.INC and PERCENTILE.INC (and numpy’s default, R’s type 7). The quartile sits at position 1 + (n − 1)×p and, when that is not a whole number, the calculator interpolates between the neighbouring values.
  • Tukey hinges — the hinges from Tukey’s Exploratory Data Analysis. The depth of the median is (n + 1)/2 and the hinge depth is (⌊that depth⌋ + 1)/2. This is the same rule as the inclusive median-of-halves method, so the two columns always agree.

A useful pattern: when n is odd, exclusive (TI-84) splits differently from inclusive / Tukey / Excel, so Q1 and Q3 often differ. When n is even, exclusive and inclusive / Tukey coincide, and Excel’s interpolation is usually the one that disagrees. The “all four methods” table under the box plot shows this for your own data. The median (Q2) is the ordinary middle value in every method here.

Worked Example: 15 Exam Scores

The calculator opens with this set of 15 exam scores, including one unusually high mark:

55, 60, 62, 65, 68, 70, 72, 75, 78, 80, 82, 85, 88, 90, 130

  1. Sort the scores (already in order) and count n = 15, which is odd.
  2. Median. The middle value is at position (15 + 1) / 2 = 8, so the median is 75.
  3. TI-84 halves (exclusive). Leave 75 out. The lower half is 55, 60, 62, 65, 68, 70, 72; its median is Q1 = 65. The upper half is 78, 80, 82, 85, 88, 90, 130; its median is Q3 = 85.
  4. Five-number summary (TI-84): 55, 65, 75, 85, 130. IQR = 85 − 65 = 20. Range = 130 − 55 = 75.
  5. Inclusive / Tukey / Excel keep 75 in both halves (and Excel interpolates at the same places on this odd-n set): Q1 = 66.5, Q3 = 83.5, IQR = 17. That is the usual “why don’t I match Excel?” gap — 1.5 points on Q1 and Q3 in this example.
MethodQ1MedianQ3IQR
TI-84 (exclusive)65758520
Inclusive / Tukey / Excel QUARTILE.INC66.57583.517

IQR, Fences and Outliers

Tukey’s rule flags a value as an outlier if it sits outside the fences

Lower fence = Q1 − 1.5 × IQR  Upper fence = Q3 + 1.5 × IQR

Values still farther out, beyond 3 × IQR, are often called extreme (or far) outliers; those between 1.5 × IQR and 3 × IQR are mild. A value that lands exactly on a fence is not an outlier — the fences are inclusive.

For the default scores with the TI-84 quartiles:

  • 1.5 × IQR fences: 65 − 30 = 35 and 85 + 30 = 115. The score 130 is above 115, so it is a mild outlier.
  • 3 × IQR fences: 65 − 60 = 5 and 85 + 60 = 145. 130 is still inside 145, so it is not extreme.

On a modified box plot the whiskers then stop at the most extreme values that are still inside the fences — here 55 and 90 — and 130 is drawn as a separate point. The fences themselves depend on the quartile method you picked: Excel’s tighter IQR of 17 moves the upper 1.5 × fence down to 109, but 130 is still the only outlier.

A large |z-score| is a different outlier rule (usually |z| > 2 or 3) and can disagree with the IQR fences, especially in a small or skewed sample. For z-scores of a data set, use the z-score calculator.

How to Draw a Box-and-Whisker Plot

  1. Draw a number line that covers the minimum and the maximum.
  2. Draw a box from Q1 to Q3. This box is the middle half of the data; its width is the IQR.
  3. Draw a line through the box at the median. The median need not sit in the centre of the box — a lopsided box is a sign of skew.
  4. For a regular box plot, draw whiskers from Q1 to the minimum and from Q3 to the maximum.
  5. For a modified box plot (the usual choice when you care about outliers, and the TI-84 option that shows dots beyond the whiskers), stop each whisker at the most extreme value that is still inside the 1.5 × IQR fences, and mark every outlier as a separate point.

The plot on this page is a modified box plot by default, with the 1.5 × IQR fences marked as dashed lines and extreme outliers drawn as diamonds. Switch to Regular if your assignment wants whiskers all the way to min and max.

Percentile Calculator

A percentile describes position. The 90th percentile is a value that about 90% of the data lie at or below; conversely, you can ask what percentile a given score is.

  • Value at a percentile. The calculator uses Excel’s PERCENTILE.INC (the same interpolation as QUARTILE.INC) and also shows PERCENTILE.EXC when it is defined. For the default scores the 90th percentile is 89.2 (INC). If you ask for the 25th, 50th or 75th percentile and you have a different quartile method selected, the tool also shows that method’s Q1, median or Q3 when it disagrees with Excel.
  • Percentile of a value. For a value inside the data range, Excel’s PERCENTRANK.INC is (position − 1) / (n − 1), interpolating when the value falls between two observations. The score 75 in the example is at the 50th percentile. The calculator also reports the midrank reading (the average of “strictly below” and “at or below”) and the raw “percent at or below” figure, which some textbooks use instead.

The TI-84 has no built-in percentile command; it only gives Q1, Med and Q3 through 1-Var Stats. Use the percentile section above for other percentages.

When n Is Even: Excel and the TI-84 Disagree

When there are an even number of observations, the TI-84, inclusive and Tukey methods all split the list cleanly in half, so they agree. Excel still interpolates, and that is usually when a spreadsheet and a calculator come apart. For the 14 commute times

10, 12, 14, 15, 18, 20, 21, 22, 24, 26, 28, 30, 35, 58

the lower half is 10–21 (median Q1 = 15) and the upper half is 22–58 (median Q3 = 28). The overall median is (21 + 22) / 2 = 21.5. IQR = 13, the 1.5 × fences are −4.5 and 47.5, and 58 is an outlier. Excel QUARTILE.INC instead gives Q1 = 15.75 and Q3 = 27.5. Paste the list into the calculator and choose Excel to see the two box plots change.

How to Find Quartiles and a Box Plot on a TI-84

The TI-84 Plus, TI-84 Plus CE and TI-83 Plus all use the same keys. You can follow along on our free TI-84 Plus CE calculator online.

1-Var Stats (five-number summary)

  1. Press STAT, 1 (Edit…). If L1 has old data, arrow up onto the L1 heading and press CLEAR, ENTER.
  2. Type each value and press ENTER after it. Use the (−) key, not the minus key, for negatives. For a frequency table, put the values in L1 and the frequencies in L2.
  3. Press STAT, arrow right to CALC and press 1 (1-Var Stats). Set List to L1 (and FreqList to L2 if you used frequencies), choose Calculate and press ENTER.
  4. Scroll down past n to read minX, Q1, Med, Q3 and maxX. For the default scores you should see Q1 = 65, Med = 75, Q3 = 85, minX = 55 and maxX = 130.

1-Var Stats always uses the exclusive median-of-halves method, even if a homework sheet or Excel used something else.

STAT PLOT (box-and-whisker plot)

  1. Press 2nd Y= (STAT PLOT), then 1 (Plot1). Turn the plot On.
  2. For a modified box plot (outliers as separate marks), choose the box-plot icon that shows dots beyond the whiskers. For a regular box plot (whiskers to min and max), choose the other box-plot icon.
  3. Set Xlist: L1 and Freq: 1 (or L2 if you used frequencies).
  4. Press ZOOM 9 (ZoomStat) to fit the window to your data.
  5. Press TRACE and use the left and right arrows to read min, Q1, Med, Q3, max and any outliers.

The calculator above builds these steps for your own numbers, including what the 1-Var Stats screen should show.

Common Mistakes

  • Comparing a TI-84 answer with Excel without checking the method. QUARTILE.INC interpolates; 1-Var Stats does not. On the default scores Q1 is 65 on the calculator and 66.5 in Excel.
  • Using the exclusive halves when the teacher asked for inclusive (or the other way round). The two only differ when n is odd.
  • Forgetting to sort the data before splitting into halves. Quartiles are defined on the ordered list.
  • Treating a value on the fence as an outlier. The 1.5 × IQR rule uses inclusive fences: equal to the fence is still inside.
  • Drawing a regular box plot when the question wants outliers marked (or the reverse). On a TI-84 that is the choice between the two box-plot icons in STAT PLOT.
  • Mixing up IQR and range. IQR is Q3 − Q1 (the middle half). Range is max − min (the full span, including outliers).
  • Using a z-score cutoff when the assignment asked for the 1.5 × IQR rule — or assuming the two will flag the same points.

Why This Quartile Calculator Is Different

  • Four quartile methods in one place — TI-84 (exclusive), inclusive, Excel QUARTILE.INC and Tukey — with a side-by-side table so you can see why two answers disagree.
  • A drawn box-and-whisker plot, modified or regular, with 1.5 × IQR fences marked and mild versus extreme outliers distinguished.
  • 1.5 × and 3 × IQR fences, not just a single “outliers” list.
  • A percentile calculator for the percentile of a value and the value at a percentile, with Excel PERCENTRANK.INC / PERCENTILE.INC and the usual textbook midrank reading.
  • Step-by-step working with your numbers and the exact TI-84 keys for 1-Var Stats and STAT PLOT, including the modified box plot that shows outliers.
  • Paste from Excel or a frequency table, dark mode, share links and a phone-friendly layout.

The standard deviation calculator remains the right tool for s, σ, variance and a histogram; this page is the one to use when the question is about quartiles, the five-number summary, IQR, outliers or a box plot. Browse every tool on the math and statistics calculators hub.

Quartile Calculator FAQ

Sort the data. The minimum and maximum are the ends. The median is the middle value (or the average of the two middle values when n is even). Q1 and Q3 are the medians of the lower and upper halves. On a TI-84, leave the overall median out of both halves when n is odd; that is the exclusive method this calculator uses by default. The five-number summary is min, Q1, median, Q3, max.

Excel’s QUARTILE.INC interpolates at position 1 + (n − 1)×p. The TI-84’s 1-Var Stats uses the median of each half and, when n is odd, leaves the overall median out. For the default 15 exam scores, Q1 is 65 on a TI-84 and 66.5 in Excel. Choose Excel QUARTILE.INC in the calculator to match a spreadsheet, or TI-84 to match 1-Var Stats.

The interquartile range is IQR = Q3 − Q1, the spread of the middle half of the data. Tukey’s rule flags a value as an outlier if it is below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR. Values beyond 3 × IQR are extreme outliers. A value that sits exactly on a fence is not an outlier. For the default scores (TI-84 method) the fences are 35 and 115, so 130 is a mild outlier.

Draw a box from Q1 to Q3, a line at the median, and whiskers out from the box. On a regular box plot the whiskers go to the minimum and the maximum. On a modified box plot they stop at the most extreme values still inside the 1.5 × IQR fences, and outliers are plotted as separate points. The calculator draws the modified plot by default, which matches the TI-84 STAT PLOT option that shows outliers.

Enter the data in L1 (STAT, 1:Edit). Press STAT, CALC, 1:1-Var Stats, and scroll down to minX, Q1, Med, Q3 and maxX. For a box plot press 2nd, Y= (STAT PLOT), turn Plot1 On, choose the modified box-plot icon to show outliers (or the regular icon for whiskers to min and max), set Xlist to L1, then press ZOOM, 9:ZoomStat. TRACE reads each number. For the default scores, 1-Var Stats shows Q1 = 65, Med = 75 and Q3 = 85.

A regular box plot always draws whiskers from Q1 to the minimum and from Q3 to the maximum, so outliers are not marked separately. A modified box plot stops the whiskers at the last values inside the 1.5 × IQR fences and plots outliers as individual points. On a TI-84 these are the two box-plot icons in STAT PLOT. This calculator defaults to the modified plot.

Excel’s PERCENTRANK.INC places a value at (position − 1) / (n − 1), interpolating when it falls between two observations. For the default scores, 75 is the 50th percentile. A common textbook alternative is the midrank: the average of the share of values strictly below the score and the share at or below it. Type the value into the percentile calculator to see both. The TI-84 itself has no general percentile command.

No. The standard deviation calculator still covers sample and population SD, variance, the mean, a histogram and z-scores, and it lists Q1 and Q3 by the TI-84 method only. Use this quartile calculator when you need a box plot, a choice of quartile methods, 1.5 × and 3 × IQR fences, or a percentile calculation.

TI 84 Calc PRO is not affiliated with or endorsed by Texas Instruments. TI-84 Plus CE is a trademark of Texas Instruments.