What Is Interquartile Range in G2 Geography Fieldwork? | Compare the Spread Between the Quartiles

Quartiles locate positions in an ordered numerical distribution. The lower quartile is associated with the 25th percentile and the upper quartile with the 75th. Their difference is the interquartile range. It is often described as the spread of the middle half of the distribution.

That wording concerns positions in the distribution, not a promise that exactly half of a small sample’s observations lie strictly between two observed values. Ties and interpolation can complicate the literal count. Keep the practical definition visible: IQR equals Q3 minus Q1. If Q1 is six minutes and Q3 is fourteen minutes, the IQR is eight minutes. It is a spread, not the interval from six to fourteen written as a pair, and not the average of the two quartiles.

A median describes the middle position of ordered values. IQR describes the separation between the quartiles. Two datasets can have the same median while differing in spread, so a single centre can hide meaningful differences in fieldwork observations.

Imagine invented journey times in two study areas. Both have a median of seven minutes, but one has an IQR of seven minutes and the other two minutes. The first has a wider quartile span under the same calculation convention. It is not enough to say that both areas have identical journey conditions because their medians match. Retain both summaries, then inspect the original observations and sampling design. A compact pair of numbers can improve a comparison while still leaving the full distribution and geographical causes unresolved.

A useful translation exercise adds three minutes to every Site A observation. Its median and both quartiles increase by three, but Q3 minus Q1 stays seven. The whole distribution moved without changing this spread. This explains why equal IQRs do not imply equal journey times: spread and level can vary independently.

The full range is maximum minus minimum. IQR is upper quartile minus lower quartile. The full range responds directly when an extreme endpoint changes, while IQR focuses on the quartile span. Neither is automatically the correct choice for every question.

Use invented readings with minimum two minutes, maximum fourteen, Q1 four and Q3 eleven. The full range is twelve minutes and the IQR seven. Both are valid, but their labels matter. If the task asks about the widest observed difference, use full range. If it asks about central spread under a specified method, IQR can be useful. A careful answer can report both rather than forcing one statistic to do every job. Do not call the IQR the average range or treat it as a second median.

Quartile calculations require ordered values. Sorting changes their arrangement, not their measured values. Keep the original dataset separately if observation order, time or site location matters to the geographical interpretation. A sorted list answers distribution questions but loses the original sequence unless identifiers are retained.

An invented unsorted list is 10, 4, 14, 2, 8, 12, 6, 4. Ordered, it becomes 2, 4, 4, 6, 8, 10, 12, 14. Check that all eight observations remain and that the repeated four has not been removed. Duplicate values are legitimate repeated observations unless there is evidence of duplicate recording. Count before and after sorting. This small check prevents a common error in which tidy-looking numerical work silently changes the dataset it claims to summarise.

There are several accepted ways to calculate sample quartiles. Methods may use different rank formulas or interpolation rules. For small samples, their results can differ. Use the convention supplied by a question, taught in the relevant course or specified by the data source.

This guide’s worked eight-value exercises use the median of the lower four and the median of the upper four. Where an odd sample is discussed, the stated exercise convention excludes the overall median before finding the two half medians. That is an explicit teaching convention, not a universal rule for every software package. If a calculator gives another answer, inspect its method before assuming that the arithmetic is wrong. Consistent methods make a comparison meaningful; unexplained switching between conventions makes it harder to reproduce.

For an even number of ordered observations, the median is the mean of the two central values under the usual median definition. In the invented eight-value record, the central values are six and eight, so the median is seven. That does not make seven the lower or upper quartile.

Mark the positions one through eight above the ordered list. The median lies between positions four and five. Under this exercise’s half-median convention, Q1 lies between positions two and three, and Q3 between six and seven. Drawing the positions helps distinguish a location in the ordered sample from the numerical value occupying that location. A position of 2.5 does not mean the measured quartile is 2.5 minutes; you must use the appropriate observations and the stated interpolation or half-median rule.

The lower half of the invented ordered eight-value record is 2, 4, 4, 6. Its middle two values are four and four. Their mean is four, so Q1 is four minutes. Keep repeated values in the list; their frequency affects the distribution.

An invented learner removes one repeated four and then finds the middle of 2, 4, 6. Although this happens to give four again, the procedure changed the sample and is not valid. A coincidentally correct answer can conceal an incorrect method. Use a second lower half, such as 2, 2, 6, 8, to see the effect: the proper median is four, while removing a duplicate changes the list. Check the method through a transparent ordered record rather than judging it solely by one numerical result.

The upper half of the invented record is 8, 10, 12, 14. The two middle values are ten and twelve. Their mean is eleven, so Q3 is eleven minutes. A quartile need not be one of the original measured values.

Keep units with the calculated quartile. Eleven minutes is a position-based summary derived from the data, not a new observed journey. If you mark it on a number line or box plot, place it between ten and twelve. Do not round it to the nearest original observation simply because no journey took exactly eleven minutes. Follow any precision instruction in the task. The distinction between an observation and a calculated summary helps avoid inventing new fieldwork records when you prepare a table or graph.

With Q3 equal to eleven minutes and Q1 equal to four minutes, IQR is 11 − 4 = 7 minutes. A non-negative spread is expected because the upper quartile is not below the lower quartile under a consistent ordered-data method.

If your IQR is negative, check whether the quartiles were reversed or incorrectly identified. Do not take an absolute value immediately and hide the source of the error. Reconstruct the lower and upper halves, check the calculation, then subtract again. A correct result is more useful when the steps can be inspected. Write the quartiles and the final IQR as separate entries, because a later question may ask for the actual quartile interval rather than only its width.

Consider the invented ordered values 1, 3, 5, 7, 9, 11, 13, 15, 17. The median is nine. For this exercise, exclude that overall median before finding the medians of the lower four and upper four. Q1 is the mean of three and five, giving four; Q3 is the mean of thirteen and fifteen, giving fourteen.

The IQR is therefore ten under this stated convention. A method that includes the overall median in each half can give different quartiles. Do not compare those results without acknowledging the convention. In an assessment, the supplied rule takes priority. In a fieldwork report, state your chosen rule so that another reader can reproduce it. This is a method issue, not evidence that the underlying measured values changed or that a calculator must be unreliable.

If many observations share a value, the quartiles can coincide. An IQR of zero means the calculated upper and lower quartiles are equal. It does not necessarily mean every observation in the sample is identical.

Use the invented ordered list 1, 5, 5, 5, 5, 5, 5, 12. Under the eight-value half-median convention, Q1 and Q3 are both five, so IQR is zero. Yet the full range is eleven. The distribution has a concentrated centre and different endpoints. Report the particular summary rather than claiming there was no variation at all. This example is useful when fieldwork values cluster because of genuine similarity, rounding or the resolution of the measurement method; inspect which explanation the evidence supports.

IQR has the same unit as the numerical variable. Journey times in minutes produce an IQR in minutes. Heights in metres produce metres. Counts produce a spread in the counted quantity. Do not square the unit or attach a percentage sign unless the variable itself is a percentage.

In an invented temperature dataset, quartiles of 24°C and 29°C produce an IQR of 5°C. These are temperature differences, not ratios saying one Celsius temperature is a percentage hotter than another. In a fieldwork table, use a full heading such as IQR of recorded journey time, minutes. A bare spread of five is too vague if several variables appear together. Clear labels are part of the calculation because they preserve what the result actually summarises.

Changing units should change the numerical spread consistently. An IQR of seven minutes is 420 seconds, because every journey time is multiplied by sixty. The median and quartiles also scale by sixty. Converting only the final label without converting the number would misrepresent the result. Check that both sites use the same unit before comparing their IQRs.

A number can be a measurement, a count, an ordered category code or an arbitrary label. Do not automatically interpret the numerical distance between response codes as a physical distance. An IQR calculated from coded categories needs careful explanation of the scale and method.

For an invented agree-disagree item coded one to five, the order of categories is meaningful, but equal numerical gaps between codes do not automatically establish equal differences in opinion. A frequency table or ordered category comparison may be clearer. For this guide’s worked tasks, journey time is a numerical measurement, so minute differences have a direct interpretation. Use the Likert response guide when interpreting coded opinions, and do not relabel a code spread as a measured amount of satisfaction.

A blank journey time may mean no observation, a failed measurement or a declined response. Zero means a recorded value of zero under the variable definition. Replacing blanks with zeros changes the ordered distribution and can alter quartiles, median and range.

Imagine an invented dataset with seven valid times and one missing observation. Calculate summaries from the valid records under the chosen method and state the valid sample size, unless the task supplies another justified procedure. Do not keep the denominator at eight while sorting only seven values. If missingness is concentrated at a difficult site or time, the remaining records may be unrepresentative. More polished statistics do not remove that coverage problem. Explain the missing-data limitation as part of the evidence rather than quietly completing the list.

IQR summarises the values included in the dataset. Whether those values support claims about a wider group depends on sampling and measurement. A perfectly calculated statistic from a narrow convenience sample can still have limited geographical reach.

In an invented journey survey, pupils observe only people arriving between noon and 12:15. Its IQR describes that recorded sample. It does not automatically describe all users across the day, especially if travel conditions or users vary by time. Use the fieldwork sampling guide to examine coverage. A strong conclusion names the sampled group and period, then considers how a broader or better-designed sample might change the distribution. Arithmetic accuracy and representativeness are separate qualities.

The invented Site A times are 2, 4, 4, 6, 8, 10, 12, 14 minutes. Site B has 5, 6, 6, 7, 7, 8, 8, 9 minutes. Both medians are seven. Under the stated half-median convention, A has Q1 four and Q3 eleven, giving IQR seven; B has Q1 six and Q3 eight, giving IQR two.

Site A therefore has the wider quartile span by five minutes. Its full range is twelve, compared with four for B. The record supports a comparison of these observed distributions. It does not prove why they differ or that A is worse under every criterion. If the question concerns typical journey duration, the equal medians matter. If it concerns consistency of observed times, the different spreads matter. State the criterion before making an evaluative judgment.

Replace the final fourteen in Site A’s invented record with one hundred, leaving all other values unchanged. The ordered list becomes 2, 4, 4, 6, 8, 10, 12, 100. Its median remains seven, Q1 remains four and Q3 remains eleven under the same convention, so IQR remains seven.

The full range rises from twelve to ninety-eight. This exercise demonstrates that this particular change affects the endpoint spread without affecting the quartile span. Do not turn it into a claim that IQR can never change when data are altered. Which observations move, sample size and quartile convention matter. Inspect the actual calculation. A robust summary can reduce the influence of some extreme values, but the extreme may still be geographically important and should remain visible in the original record.

For comparison, the original Site A total is sixty and its mean is 7.5 minutes. Replacing fourteen with one hundred increases the total by eighty-six to 146, giving a mean of 18.25 minutes across eight observations. This original exercise shows why reporting the unchanged median and IQR alone would conceal an important change in the tail.

One common box-plot rule uses fences at Q1 minus 1.5 times IQR and Q3 plus 1.5 times IQR. Values beyond those fences are flagged as potential outliers under that convention. This is a screening rule, not proof of a recording error or a universal requirement for every Geography task.

For invented Site A, the fences are 4 − 1.5 × 7 = −6.5 and 11 + 1.5 × 7 = 21.5 minutes. The modified value of one hundred lies above the upper fence. Flag it for checking. The negative lower fence is a mathematical boundary; it does not imply a physically negative journey time was observed. Follow the question’s rule when supplied and distinguish the calculated fence from the actual minimum, maximum and whisker endpoints.

A flagged observation might reflect a transcription error, a different situation or a genuine extreme within the intended population. Investigate its provenance before deciding how to handle it. Removing inconvenient observations simply to make a pattern tidier undermines the analysis.

In an invented journey record, one hundred minutes could arise from a misplaced digit, a major delay or a respondent including a stop that others excluded. Each possibility calls for a different response. Check the original record and variable definition where feasible. If the value is valid, retain it or explain a justified analytical treatment. If it is corrected, preserve the reason. The mean and median guide helps compare how different summaries respond to unusual values without pretending those values have no importance.

A box commonly runs from Q1 to Q3 with a median line inside. Whiskers are not identical in every box-plot convention. Some displays use minimum and maximum; others use the most extreme observed values within specified fences and plot further values separately.

For the modified invented Site A record, a fence-based display could show one hundred as a separate point and the upper whisker at twelve, the largest remaining value within the upper fence of 21.5. The whisker need not end at 21.5 because that fence is not an observation. Read the legend. A learner who assumes every whisker is the full maximum may overlook the separate outlier point. Explain which convention the graph uses before comparing its apparent full spread with a numerical range.

A median and IQR provide useful summaries, but they do not show all clusters, gaps, tail behaviour or the number of observations. Different datasets can share these summaries while having different shapes. Retain the original data or an appropriate distribution display when those features matter.

An invented fieldwork report might compare two sites using box plots and then inspect dot plots for clusters. The first view supports a compact centre-and-spread comparison; the second preserves individual values more visibly. Do not infer a normal distribution merely because a box looks balanced. Nor does a wider IQR establish two distinct groups. Match the claim to the display. Summary statistics help organise evidence; they should not replace inspection of the observations and sampling design that produced them.

Sample size should remain visible on a display. Two boxes of equal width on a page do not necessarily represent equal numbers of observations. If one site has eight measurements and another eighty, read that difference before judging the strength of the comparison. Box dimensions alone do not supply the study’s sampling effort or coverage.

The IQR of combined data is calculated from the combined ordered observations under the chosen convention. It is not generally the arithmetic mean of the separate group IQRs. Quartile positions depend on the full distribution, including the relative group sizes and levels.

Try an invented simple example: Group C contains 1, 1, 1, 1 and Group D contains 9, 9, 9, 9. Each group has IQR zero. Pooled, the eight values have Q1 one and Q3 nine under the half-median convention, giving IQR eight. Averaging the group IQRs would wrongly produce zero. This example explains the structural issue without advanced formulas. Keep group comparisons and pooled summaries as separate calculations, and use the raw observations when a combined statistic is required.

Before using a spreadsheet or calculator output, check the input range, missing values and quartile function or convention. Different functions may use different definitions. A label saying quartile does not guarantee agreement with the method required by a school task.

Use the invented eight-value record as a manual check. Record your half-median result, then compare a tool’s documentation and output. If they differ, explain the method difference rather than changing one answer without understanding why. Also inspect whether the software treated a blank as missing, ignored text or included an unintended total row. These input issues can be more consequential than the quartile convention. A reproducible fieldwork report identifies the data used and the calculation method, not merely the name of the device that displayed a number.

A model using invented data could read: Both sites had a median recorded journey time of seven minutes. Site A’s IQR was seven minutes, compared with two at Site B under the same quartile convention. A therefore had a wider central spread in the observed sample, although the typical value measured by the median was equal.

Continue with the study scope: the samples were collected during a short period, so the comparison cannot automatically represent all users or times. An explanation for the spread would need route, timing or user evidence. This paragraph separates statistical description from geographical cause. In an assessment, use the requested level of detail, preserving the units, comparable method and criterion. A wider spread is an observation; whether it is beneficial or problematic depends on what the investigation is evaluating.

Check that values are ordered, all valid observations are retained, the quartile convention is stated and units are correct. Calculate Q1 and Q3 before subtracting. Keep the sample size and collection scope beside the result. Inspect unusual values rather than deleting them automatically.

Test yourself on the worked pair: equal medians do not imply equal IQRs. Changing one extreme can greatly alter the full range while leaving this sample’s IQR unchanged. Averaging group IQRs does not generally produce a pooled IQR. If these distinctions are clear, continue to mean and median, sampling and evidence interpretation. The useful goal is a supported comparison: show what the selected data says about centre and spread, then explain what further geographical evidence is needed to understand the pattern.

A final reverse calculation checks the relationship: if Q1 is nine metres and IQR is six metres, Q3 must be fifteen metres. If Q3 is twenty and IQR eight, Q1 is twelve. These tasks confirm the quartile difference without requiring a new dataset or an unstated convention for locating the quartiles.