Why Careful Preparation Matters
A quantitative graph represents recorded measurements. If the values are entered in inconsistent units, rounded without reason, or silently altered, the graph no longer faithfully represents the data. Before choosing or drawing a display, a useful first step is to check what each measurement means and whether it can be used as recorded.
Imagine collecting commute times from students traveling to campus. One person reports minutes, another reports hours, and two students report the same time. Those repeated values are not redundant records: they may represent two different students who happened to have the same commute time. A blank response is not a zero, and a very large value is not automatically an error. Each entry needs a careful, documented decision.
Start With the Variable and Its Units
Before examining individual values, specify what is being measured. For example, “commute time” could mean time from leaving home to arriving at campus, time spent in transit, or the total time from leaving home until reaching a classroom. Those definitions can produce different answers. A data set should use one clear definition, and its units should be identified explicitly, such as minutes.
A unit is part of the meaning of a measurement. A recorded value of 15 without a unit is ambiguous: it might mean 15 minutes or 15 hours. If all observations are intended to be in minutes, an entry recorded in hours must be converted before values are treated as one consistent set.
For a time measured in hours, the conversion to minutes is:
The factor 60 converts the unit, not the commute itself. For example, \(0.25\) hours is \(0.25 \times 60 = 15\) minutes. The recorded value can then be written in the common unit, with a note that it was converted. Converting units preserves the represented amount of time; it does not justify changing the observation to a different amount.
Worked Example: Converting a Reported Unit
A hypothetical campus survey defines commute time as the elapsed time from leaving home until arriving at campus. The working data sheet uses minutes, but one student reports a commute of \(0.4\) hours. Convert this entry to minutes.
Use \(t_{\text{minutes}} = 60t_{\text{hours}}\):
Record the observation as 24 minutes and note that the original response was \(0.4\) hours. This is a unit conversion, not a change to the reported duration. If the source unit had not been known, the value could not safely be converted; the correct step would be to clarify or flag it, not guess.
Keep Repeated Values and Recorded Precision
Each measurement belongs to an individual. If two students each report a commute of 12 minutes, the data contain two observations of 12 minutes. Removing one because it duplicates the other would reduce the sample size and change the distribution of recorded values. A duplicate value is not the same thing as a duplicate record: the first is a repeated measurement value, while the second would mean the same individual or response was entered more than once.
The digits recorded also matter. A report of 17.5 minutes conveys a different level of recorded precision from a report of 18 minutes. Unless a clear rule requires otherwise, retain the values as recorded; do not round all observations just to make them look alike. Rounding can make distinct observations appear equal or can change a value used in a later graph. The axis or data record can show appropriate precision without altering the underlying observations.
Recorded precision is not a guarantee of measurement accuracy. A value written as 17.5 minutes indicates that the report was recorded to a tenth of a minute; it does not prove that the actual commute duration was known to within exactly one tenth of a minute. For graphing, the key practice is to preserve what was recorded and to avoid claiming more precision than the measurement process supports.
Worked Example: Preserving Repeated Values
A hypothetical group of six students reports commute times, all in minutes: 8, 12, 12, 17.5, 17.5, and 24. Prepare the list for use as quantitative data.
There are six observations, one for each student. The two reports of 12 minutes remain two entries, and the two reports of 17.5 minutes also remain two entries. The prepared list is still:
The number of observations remains \(n=6\). Replacing each pair of repeated values with one entry would incorrectly leave only four observations. Rounding 17.5 to 18 would also change the recorded values, so it is not part of preparation unless a stated analysis plan specifically requires that rounding.
Missing, Impossible, and Unusual Values
A blank entry means no usable value was recorded. It does not mean zero minutes, and it should not be replaced with zero or with a typical commute time. Mark it as missing according to the data system being used, and keep track of how many observations are available for the graph. If a response is recorded with a code such as “NA,” make sure that code is treated as missing rather than as a numerical observation.
An impossible value conflicts with the variable’s definition or the measurement rules. For example, if the variable is elapsed commute time, a reported value of \(-4\) minutes is impossible: elapsed time cannot be negative. But a value that seems surprising is not necessarily impossible. A commute of 150 minutes may be unusual, yet it could be genuine for a student who lives far away. The appropriate response is to check it against the source or survey rules, not to delete it solely because it looks extreme.
A practical distinction is:
- Missing: no numerical observation is available.
- Impossible: the entry cannot be a valid value under the variable’s definition or stated rules.
- Unusual: the entry is uncommon or surprising, but may still be valid.
When an entry is flagged, preserve the original response and record what was checked and what decision was made. If the source confirms a transcription error, correct it using the source and document the correction. If the value cannot be resolved, keep it flagged or treat it as unavailable according to the analysis plan. Do not quietly substitute a value or discard a plausible observation.
Worked Example: Reviewing a Mixed Set of Entries
In a hypothetical survey, the commute-time field is intended to contain elapsed time in minutes. Six response cells contain: 9, 14, blank, \(-3\), 140, and 9. The survey defines a commute as travel from a student’s home to campus. Decide how to handle each entry before graphing.
The first 9 and the second 9 are two recorded observations. Keep both because they may belong to different students. The 14 is also a usable value. The blank is missing; do not enter 0 in its place.
The value \(-3\) is impossible as an elapsed time, so flag it and check the original response. It should not be included as a valid commute duration unless the source reveals a correction. The value 140 is long, but the survey definition alone does not make it impossible. Check it against the source if possible; if it is confirmed, retain 140 minutes. Therefore, it would be unjustified to remove 140 merely because it is larger than the other values.
A Short Justification for Consistent Units
Converting every valid time to one unit allows the numerical values to be compared on the same scale. If \(t\) is a time in hours and \(m=60t\) is the corresponding time in minutes, then multiplying by the positive number 60 preserves order:
Thus a commute that takes longer in hours also takes longer after conversion to minutes. The numbers change because the unit changes, but the underlying ordering and durations do not. This is why a conversion is appropriate when its source unit is known, while arbitrarily changing, rounding, or replacing a valid value is not.
A Reliable Preparation Routine
A brief audit can prevent avoidable errors before any quantitative display is constructed. Keep the original records available and make a separate prepared copy if values need conversion or invalid entries need flags. For each variable, work through the following sequence:
State exactly what the value represents and identify its unit, such as elapsed minutes from home to campus.
Convert a known alternative unit using the appropriate conversion factor, and retain a note of the original response.
Keep repeated values and the precision recorded; do not round or remove entries without a defined reason.
Keep blanks distinct from zeros, investigate impossible values, and check surprising values rather than automatically deleting them.
Record conversions, confirmed corrections, unresolved entries, and the number of usable observations.
Common Mistakes
- Mixing units: treating \(0.5\) hours and 30 minutes as different amounts, or entering both numbers without converting to a common unit. Convert only when the original unit is known.
- Removing repeated values: assuming identical values must be duplicate records. Keep each valid measurement for its own individual.
- Turning missing into zero: interpreting a blank response as a zero-minute commute. Record it as missing unless the source explicitly reports zero.
- Rounding too early: changing recorded values to make a list look simpler. Retain valid values at their recorded precision unless a justified, stated procedure calls for rounding.
- Deleting an unusual value automatically: confusing “surprising” with “impossible.” Check the source and the variable definition before deciding whether a value is invalid.
The central principle is to make the data usable without making them different. A careful record of units, repeated values, precision, and flagged entries makes a quantitative graph more faithful to the observations it represents.
Check Your Understanding
For each question, focus on preserving what the measurements mean.
- A student reports a commute of \(0.3\) hours, and the data sheet uses minutes. What value should be recorded in minutes, and what calculation gives it?
- Five students report 10, 10, 12, 15, and 15 minutes. How many observations should be retained? Explain why.
- A blank commute-time cell appears in a data set. Why is entering zero not an appropriate default?
- A commute-time response is \(-2\) minutes. What makes this different from a very long, positive response?
- A value is recorded as 18.7 minutes. What should be considered before rounding it to 19?