Variation and Spread
Three sentences on variation, an illustration containing no measurement of any kind, and one inverse relationship. Here is what that gives you, and precisely what it leaves you to find elsewhere.
What the week actually says about variation
Three sentences, and they do three different jobs. The first is an illustration and a claim about the relationship between two ideas. The second is the closest thing the slide gives to a definition of variation. The third is a methodological instruction, and it is the most useful line on the slide.
Taken together they establish something a practising manager can act on immediately: variation is a property of repeated instances of the same activity, and you cannot see it in one instance. That is a genuinely transferable idea and it is worth separating from the material's failure to quantify it.
The illustration, and what it contains
As an example it works, and it is worth knowing why. It fixes the idea that variation belongs to a set of repeated experiences rather than to any one of them; that the differences worth noticing may be subtle rather than dramatic; and that a reasonable person forms a judgement about consistency without ever computing anything.
What it cannot do is show you how to move from that judgement to a number. Nothing is measured, so nothing demonstrates measurement, and the slide that follows offers no calculation either. If you were looking for the moment in the week where an intuition about spread becomes a statistic, this is where you would expect to find it, and it is not here.
Consistency, and the one relationship the slide states
The relationship, quoted exactly: "the lower the variability the higher the consistency". It is stated as an inverse relation, and it is the only relationship of any kind stated on the slide.
It is also the most useful translation in the material for anyone reporting to a delivery audience, because consistency is a word a project sponsor already owns. A process that is highly variable is a process that is inconsistent, and saying it that way conveys the finding to people who will never read a chart.
The overall pattern, not the single point
The third sentence is the one to take away: "In looking at some of the possible causes of variation it is necessary to understand the overall pattern of variation and not just the information contained in a single point." It is the same instinct that runs through the week's reading procedure, where the first question you put to a display is about its overall shape — see Reading a Graphical Display.
Three words for one idea, and no measure attached to any of them
The week uses three different words for what is recognisably the same property of a set of measurements, across two slides, and never reconciles them. Two of the three appear in consecutive sentences on the same slide.
THE THREE WORDS AGAINST WHAT THE WEEK SUPPLIES FOR EACH
| Word | Where it appears | What it is attached to | Definition |
|---|---|---|---|
| Spread | The distributions slide, twice | Named as one of three key features of a distribution, and as something you would want "some measure" of in order to summarise patterns | None |
| Variability | The variation slide, first sentence | Related inversely to consistency, through the illustration | None |
| Variation | The variation slide, second and third sentences | "the differences observed from repeated experiences of a wide range of activities"; then a methodological instruction about its overall pattern | A characterisation, not an operational definition |
The slide gives no statement that variability and variation are the same word for the same thing, and no statement that they are not. Neither is connected to the spread named three slides earlier.
The absence, stated precisely
The distributions slide names three key features of a distribution — shape, location and spread — and states the count as three, which the list beneath it matches. It then says that in order to summarise patterns you would be interested in some measure of location, glossed as perhaps an average or median, "and also some measure of spread".
For location, the week does supply something: three averages are defined in its terminology table, however unevenly, and they are set out at Measures of Central Tendency. For spread, it supplies nothing. Not on that slide, not in the eight-term terminology table — which covers two branches of statistics, central tendency and its three measures, a count and a display — and not on the variation slide three slides later. Of the three key features it names, the week supplies a measure for one.
One further absence belongs here. The slide says "In looking at some of the possible causes of variation" and names no cause. No distinction between random and systematic variation, between measurement error and true differences in the thing measured, or between variation within a case and variation between cases appears anywhere in the week. A reader who needs to explain in a discussion chapter why their measurements differ has no vocabulary for it from this material.
What to go and learn, and how to work until you have
The list below is what a second source has to give you before you can quantify anything on this page. Take it to a statistics or research methods text, work through every line, and cite that text — not this material — for whatever you end up reporting.
The itemised gap: what a second source must supply
- A named measure of spread, and a statement of what quantity it actually measures
- How it is computed from a set of observations, and what units the result is expressed in
- How it behaves when a distribution is skewed or contains an extreme value — the week's own extreme-value example shows an average destroyed by one respondent and never draws the lesson
- Which measure of spread belongs with which measure of location, since the week defines three averages and pairs them with nothing
- How to report a measure of spread beside an average in a table, which the week's table rules never mention
- Whether more than one measure is conventionally reported together, and what each adds
- Which measure the readers of your discipline expect to see, and how to state it so they can check it
What you can defensibly say from this material
- That spread is one of three key features of a distribution
- That variation is what shows up across repeated experiences of the same activity
- That lower variability means higher consistency
- That the overall pattern of variation, not a single point, is what you interpret
- That your description of variation is qualitative, because the material supplies no measure
What you cannot say from it
- How much your data vary, in any unit
- That one set of observations is more variable than another
- That an average you have reported is or is not representative
- That a value is far enough from the centre to be treated as unusual
- That your data are consistent enough to support a decision
Working while the gap is still open
What to carry forward
- Spread is declared one of three key features of every distribution, a measure of it is called for twice, and no measure of it appears anywhere in the week. That is the finding.
- What the material does give you is usable: variation is what you see across repeated experiences, consistency is its inverse, and the overall pattern is what you interpret, never a single point.
- The illustration contains no measurement of any kind, which is why it cannot bridge from the intuition to a number.
- Three words — spread, variability, variation — are used for one idea across two slides, and the material never says whether they are the same.
- Get a measure from a cited text before you claim anything quantitative about consistency, and say in your limitations that the taught material supplied none.
Frequently asked questions
Which measure of spread does this material tell me to use?
None. It names spread as one of three key features of a distribution, asks twice for "some measure of spread", and never names one anywhere in the week. This page does not nominate one either, because doing so would attribute guidance to material that does not contain it.
What does the material actually say about variation?
Three things. That variation relates to the differences observed from repeated experiences of a wide range of activities; that the lower the variability the higher the consistency; and that in looking at possible causes you must understand the overall pattern of variation rather than the information in a single point.
Are variation and variability the same thing here?
The material does not say. It uses variability in one sentence and variation in the next two, defines neither operationally, and never connects either to the spread it named three slides earlier. Treat them as one idea if you must, and note in your writing that the source does not settle it.
Can I use the consistency claim in a report?
As a description, yes — it is the most communicable idea on the slide, because consistency is a word a sponsor already understands. As a quantified claim, no: neither variability nor consistency is measurable from this material, and no example of establishing the relationship is given.
Why does the week use standard deviations in its one rule but never define a measure of spread?
The deck never explains it. Its normal-distribution slide is expressed entirely in standard deviations from the mean, four times, and the term appears in none of the week's definitional slides. The variation slide then arrives two slides later with no measure and no reference back to the rule that assumed one.
What should I put in my limitations section about this?
That the taught material named spread as a key feature of a distribution without supplying any measure of it, and that the measure you used was taken from a named second source. Stating it accurately protects the rest of your analysis and is more credible than silence.
References and source attribution
- Veal, A. J. 2005, Business Research Methods: A Managerial Approach, 2nd ed., Longman. — the sole entry on the week's reference slide. It is cited for the normal-distribution slide, and the variation slide carries no attribution at all.
- A publisher's companion website for a fourth-edition social research text, cited on the week's terminology slide as a bare address with no author, year or title stated. It supplies the week's eight definitional terms, none of which is a measure of dispersion.
- The supplied teaching source: the week 11 slide deck on analysing data and the presentation of quantitative data, whose variation slide and distributions slide are reproduced on this page. No study notes for this week were supplied.
Suggested questions for Ask KEVOS
- What does the supplied material say about variation, and what does it leave out?
- Help me describe the spread in my results without claiming to have measured it.
- Draft a limitations paragraph about the measures this teaching material does not supply.
- How do I explain consistency to a sponsor who will not read a chart?
- What should I ask a statistics text for before I report anything about variability?