Free graphing resources · Original practice
Draw four box plots from minimum, Q1, median, Q3 and maximum. Calculate range and IQR while keeping the supplied five-number summary visible.
Draw four box plots from minimum, Q1, median, Q3 and maximum. Calculate range and IQR while keeping the supplied five-number summary visible.
Choose Letter or A4, then download a student sheet first. Keep the separate reference or answer file closed until you have attempted the case. Every worksheet, SVG and answer is free without signup.
Original worksheet collection. Letter or A4 PDF and editable SVG.
Original worksheet collection. Letter or A4 PDF and editable SVG.
Original worksheet collection. Letter or A4 PDF and editable SVG.
Original worksheet collection. Letter or A4 PDF and editable SVG.
Complete free PDF pack.
| Case | Focus |
|---|---|
| BX01 | Even middle spread |
| BX02 | Tight middle half |
| BX03 | Wide upper half |
| BX04 | Negative to positive |
All examples use original fictional data and coordinate units. They are practice material, not measured classroom results, published questions or evidence about real people.
BX01: Even middle spread
| Check | Worked result |
|---|---|
| 1 | Min=1; Q1=3; median=5; Q3=7; max=10. |
| 2 | Range 9; IQR 4. |
| 3 | Whiskers run from minimum to Q1 and Q3 to maximum. |
The first case shows the checking pattern. Individual answer files contain the completed graph and result for every case.
Begin by identifying the five specific values provided for your chosen case, such as minimum, first quartile, median, third quartile, and maximum. These numbers are fixed fictional data points that dictate the entire diagram. Do not calculate new statistics or apply outlier rules, as the supplied values alone control the visual output. Confirm that you have the correct set, like the even middle spread or negative to positive examples, before drawing. This step ensures that your subsequent geometric construction aligns perfectly with the listed coordinates defined in the original resource files, preventing misalignment during the manual plotting process.
Draw a horizontal line and mark the scale based on the minimum and maximum values of your selected case. For instance, if the range spans from negative six to eight, ensure the spacing accommodates both extremes clearly. Label the axis with appropriate intervals to maintain proportionality. This foundational step requires careful attention to distance, as the box and whiskers must fit within these boundaries. The scale must reflect the exact numerical distance between the lowest and highest points provided in the fictional dataset, ensuring the final box plot accurately represents the spread without distortion or compression of the visual space.
Using your scaled line, draw a rectangular box extending from the first quartile to the third quartile. Inside this box, draw a vertical line at the median position. Extend horizontal whiskers from the box edges to the minimum and maximum values. Ensure the whiskers connect directly to the box sides. This geometric arrangement visually represents the distribution defined by the five numbers. Since no outlier rules apply, the whiskers always reach the extreme values. Check that the median line divides the box according to the specific quartile positions, creating a clear visual summary of the fictional data structure.
| Watch for | Check instead |
|---|---|
| Applying standard outlier detection rules to trim the whiskers. | Ignore outlier rules entirely. The whiskers must extend exactly to the supplied minimum and maximum values, regardless of distance from the quartiles, as the five given numbers fully define the diagram. |
| Calculating new quartiles from raw data instead of using provided values. | Use only the five specific numbers given in the case file. These are fixed fictional values that determine the box and median positions directly, so no additional statistical computation is required or permitted. |
| Assuming physical print dimensions match digital coordinate scales. | Rely on the relative positions of the five numbers on your drawn line. Physical printing checks are not performed, so focus on the logical spacing derived from the digital coordinates rather than absolute paper measurements. |
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Minimum, Q1, median, Q3 and maximum. The box spans Q1 to Q3.
The interquartile range is Q3-Q1.
No. These cases use the supplied five-number summary directly.
Yes. The individual student, reference and answer files plus collection packs are free without signup. Credit Zumola under CC BY 4.0 when sharing or adapting.
Quartiles split ordered data into four groups, but there is more than one accepted convention. One common school method finds the median, then takes the median of the lower half and the median of the upper half; when the count is odd, the overall median is excluded from both halves. Another convention uses position formulas on the full ordered list. Both can be legitimate, but a worksheet answer must say which one it used, because Q1 and Q3 can differ by one data step.
Write the ordered list first, number the positions, and mark the median position. Then apply one stated rule consistently to every case on the page. If a value repeats, keep every copy; duplicates are data, not errors. Record Q1, median and Q3 as actual data values or as midpoints between two values, and say which.
The interquartile range is Q3 minus Q1. It measures the spread of the middle half only, so it ignores the tails. Report it in the same units as the data and keep the subtraction visible so a reader can recheck it.
A common outlier test uses fences: lower fence = Q1 − 1.5 × IQR and upper fence = Q3 + 1.5 × IQR. Values strictly beyond a fence are flagged as outliers under that rule; values exactly on a fence are not. State the multiplier you used, because 1.5 is a convention, not a law.
Whiskers then reach the most extreme values that are not flagged, while flagged points are drawn separately. This keeps the box and whiskers describing the bulk of the data. If you choose to extend whiskers to the minimum and maximum instead, say so plainly and do not call distant points outliers.
Check that every original value is accounted for exactly once: inside the box region, on a whisker, or as a plotted outlier. A count that does not match the raw list signals a transcription slip.
Read your finished plot back into a five-number summary and compare it with your calculation sheet. If the read-back differs, the drawing is wrong even when the arithmetic is right. Check axis scale: equal spacing between labelled ticks, and a range that includes outliers without crushing the box.
Label the axis with units and note the quartile convention and outlier multiplier beside the plot. A reader should be able to reconstruct your decisions without guessing. Where two valid conventions exist, a short note prevents a correct answer from looking wrong.
Data: 3, 5, 6, 8, 9, 11, 14, 15, 22. Use the rule that excludes the overall median from both halves, and flag outliers beyond 1.5 × IQR.
Nine values, so the median is the 5th value, 9. Lower half: 3, 5, 6, 8, giving Q1 = (5 + 6) ÷ 2 = 5.5. Upper half: 11, 14, 15, 22, giving Q3 = (14 + 15) ÷ 2 = 14.5. IQR = 14.5 − 5.5 = 9. Lower fence = 5.5 − 13.5 = −8; upper fence = 14.5 + 13.5 = 28. No value lies beyond either fence, so no outliers are flagged. Whiskers reach 3 and 22. Five-number summary: 3, 5.5, 9, 14.5, 22. All nine values are accounted for.
Yes, when different quartile conventions or outlier multipliers are declared. The plots are comparable only if the stated rules match.
Under the usual strict test, no. Only values beyond the fence are flagged; state this boundary explicitly.
The box spans Q1 to Q3, so its width is the IQR and it covers the middle half of the ordered values, not the middle half of the axis.
