Measures of Central Tendency
Three one-line definitions in a table with no headings, sourced to a bare web address, in a week where no average is calculated on any data at any point. What the table says is here in full, including the row that defines the general idea as one of its own three parts.
The four rows, exactly as the table gives them
These four definitions are the whole of the supplied material on averages. They arrive as four rows of an eight-row table on a single slide, with no lead-in sentence, no worked figure and no example.
THE CENTRAL TENDENCY ROWS, QUOTED VERBATIM
| Term | Definition as given | What a reader can do with it |
|---|---|---|
| Central tendency | "Most common value for variables measured at a nominal level" | Identifies a most-common value. Does not describe a general concept, and does not cover variables measured at any other level. |
| Mean | "The weighted average calculated by totalling the value of all the cases and dividing by the total number" | The procedure is followable. The label it is given describes a different statistic - see below. |
| Median | "The point that divides the distribution in half" | States what the median is. Does not state how to find it. |
| Mode | "Most popular value" | Two words. Cannot express a distribution with two peaks, which the same deck later asks you to look for. |
The table has no column headings in the source. Its stated source is a publisher's companion website for a fourth-edition social research text, cited as a bare web address with no author, year or title.
The concept and one of its measures share a definition
The first row defines central tendency as the most common value for variables measured at a nominal level. The last row defines the mode as the most popular value. The two denote the same quantity, and the table contains both.
What the table's structure implies
- Central tendency heads a group of rows.
- Mean, median and mode follow it.
- Each of the three locates a centre differently.
- That arrangement reads as a concept followed by its measures.
What the table's wording says
- Central tendency is "Most common value for variables measured at a nominal level".
- Mode is "Most popular value".
- The two descriptions pick out the same quantity.
- So the concept is defined as one of the three measures beneath it.
The mean: a label and a procedure that do not match
This is the second definitional problem in the same table, and it is contained in a single sentence. The sentence names one statistic and describes another.
THE ONE SENTENCE, SPLIT INTO ITS TWO HALVES
| Half of the definition | What it says | Status in the deck |
|---|---|---|
| The label | "The weighted average" | No weight is mentioned, defined or exemplified anywhere in the week. Nothing tells a reader what would be weighted or by what. |
| The procedure | "calculated by totalling the value of all the cases and dividing by the total number" | Followable as written. The procedure supplies no mechanism for treating any case differently from any other. |
The source does not say which of the two governs, and this page does not choose. If you use the definition, quote both halves or use a definition from a text you cite.
In practical terms the risk is small but specific: a reader who takes the label at face value will believe the material has taught them a weighting method, and it has not. A reader who follows the procedure will produce a number, and the material never shows one being produced.
The median: a location with no procedure
That states what the median is. It does not state how to obtain one, and the three things a reader would need in order to get a median out of a column of numbers are each absent.
The mode: two wordings, and no vocabulary for two peaks
The mode is defined as the "Most popular value". Three rows above, the same quantity is described as the "Most common value". The wordings are different and the deck does not say whether the difference is meant.
The sharper problem is what neither wording can express. Later in the same deck, the guidance on reading a chart asks "Is there one or more than one clear peak?" and treats more than one peak as diagnostic - a possible sign that the data are a mixture from two or more sources. A definition that identifies a single most popular value has no way of describing that situation, and the words that would describe it do not appear anywhere in the week.
Location and central tendency: two names, seven slides apart
Later in the deck, a slide on modelling data names three key features of a distribution - shape, location and spread - and glosses location as "perhaps an average or median". That is the same idea the table calls central tendency, and the deck never says so.
THE TWO NAMES AND THEIR TWO GLOSSES
| Name | Where | Gloss given | Which measure it points at |
|---|---|---|---|
| Central tendency | The eight-term table | "Most common value for variables measured at a nominal level" | The mode |
| Location | The modelling-data slide | "some measure of location of the distribution (perhaps an average or median)" | The mean or the median |
Two names for one idea, with glosses pointing at different measures. The deck reconciles neither, and this page records both rather than choosing.
The same slide calls for "some measure of spread" alongside the measure of location, and no measure of spread is named anywhere in the week - which is the subject of Variation and Spread.
Nothing is ever calculated
The three measures are defined and none is computed. There is no dataset in the week, no column of figures, no arithmetic and no result. No formula, symbol or equation appears anywhere in the deck; the one mathematical rule in the entire week is a charting rule of thumb for choosing the number of classes in a histogram, covered at Presenting Data in Graphs.
Reporting an average in a project report
The material supports a small number of moves cleanly, and it is worth being clear about which are yours and which are the source's.
What to state whenever you report an average
- Which of the three measures you are reporting, in the word rather than by implication.
- The number of cases it was computed over.
- Whether any cases were excluded before you computed it, and on what rule.
- The definition you worked to and the text you took it from, if the definition matters to the argument.
- These four items are guidance beyond the source. The supplied material states none of them; what it states is the three definitions above.
What to carry forward
- Central tendency and the mode are given the same definition in one table, and the general sense of the concept is not available anywhere in the supplied material.
- The mean's label says weighted average and its procedure says otherwise. Quote both halves or take the definition from a text you cite.
- The median is defined without a procedure: no ordering, no even-numbered case, no statement of whether it is an observed value.
- "Most popular value" cannot describe a distribution with two peaks, and the same deck asks you to look for exactly that.
- Three measures defined, none computed, no formula in the week. Any calculation you perform is yours, and should be reported so that a reader can reproduce it.
Frequently asked questions
What is central tendency, according to this material?
The supplied table defines it as "Most common value for variables measured at a nominal level", which is the same quantity it defines three rows later as the mode. There is no definition of central tendency as a general idea anywhere in the supplied material, so citing it for one means citing it for a definition of the mode.
Is the mean in this material a weighted average or an ordinary one?
The one sentence says both. It calls the mean "the weighted average" and then describes totalling the value of all the cases and dividing by the total number, a procedure in which no case is treated differently from any other. No weight is mentioned, defined or exemplified anywhere in the week, and the source does not say which half of its own sentence governs.
How do I calculate a median from this material?
You cannot. The definition given - the point that divides the distribution in half - states what a median is without stating how to obtain one: it does not tell you to order the values, does not address an even number of cases, and does not say whether the median must be a value that occurred in your data. Take the procedure from a methods or statistics text and cite it.
Which average should I report?
The supplied material does not say. It defines three, instructs you elsewhere to provide averages for rows and columns of a table where appropriate, and never states what makes one appropriate. Its own example of an average distorted by one extreme respondent leaves the word "averaged" unexplained, so the choice is yours to make and to justify.
What if my data have two peaks?
The material asks you to look for that on a chart and gives you no vocabulary for it. Its definition of the mode is "Most popular value", which identifies one value, and the words that describe a two-peaked distribution do not appear anywhere in the week. The reading guidance suggests more than one peak may mean the data are a mixture from two or more sources, and stops there.
Are location and central tendency the same thing here?
They appear to be, and the deck never says so. One slide names location as one of three key features of a distribution and glosses it as perhaps an average or median; the definitional table calls the idea central tendency and glosses it as the most common value at a nominal level. Two names, seven slides apart, pointing at different measures, with no statement connecting them.
References and source attribution
- Veal, A. J. 2005, Business Research Methods: A Managerial Approach, Longman - the one work with complete bibliographic data cited in the supplied quantitative week.
- Bryman, A. 2016, Social Research Methods, 5th ed., Oxford University Press, Oxford - cited elsewhere in the supplied source; a place to obtain the computational procedures this week does not supply.
- O'Leary, Z. 2017, The Essential Guide to Doing Your Research Project, 3rd ed., Sage Publications, London.
- Naoum, S. G. 2013, Dissertation Research & Writing for Construction Students, 3rd ed., Routledge.
- The supplied teaching source: the quantitative analysis and presentation slide deck, slide 13 and the modelling-data slide. The eight-term table on slide 13 is attributed on the slide to a publisher's companion website for a fourth-edition social research text, cited as a bare address with no author, year or title. The week's study notes are listed in the upload manifest and are not present in the supplied files.
Suggested questions for Ask KEVOS
- Give me cited definitions of mean, median and mode to use alongside this material.
- Which measure of central tendency should I report for a five-point agreement scale?
- Show me how to compute a median for an even number of cases, with a citation I can use.
- Draft a results paragraph reporting an average from a survey of forty project managers.
- What vocabulary do I need to describe a distribution with two peaks?