Chapter 3 Measures of Central Tendency
3.1 Mode
Central tendency is the information about the clustered-ness of a variable’s distribution; whether its observations/cases/responses tend to group together (or not) and where (i.e., in which categories/values) they tend to fall.
There are three measures of central tendency: mode, median, and mean. In this section, we explore the mode.
To find a variable’s mode, you only need a frequency table – or rather, even just the frequency column in the table (although the Valid Percent column will do you just as well). Here is a simple, small-N, real-world example.
Example 3.1 Religious Affiliation of Canadian Prime Ministers
Table 3.1 Religious Affiliation of Canadian Prime Ministers (Wikipedia 2017)
| Religious affiliation | Frequency |
| Anglican | 4 |
| Baptist | 3 |
| Evangelical | 1 |
| Presbyterian | 3 |
| Roman Catholic | 10 |
| United Church of Canada (prev. Methodist) | 2 |
| TOTAL | 23 |
What is the most popular religious affiliation of Canadian Prime Ministers as of 2019? Or, what religious affiliation is most frequently reported by Canadian Prime Ministers so far? In other words, what religious affiliation do Canadian Prime Ministers most have tended to have?
Surprising no one with any knowledge about Canada, the largest category among the religious denominations, or the one that Canadian Prime Ministers most frequently subscribe to — i.e., the category with the highest frequency — is “Roman Catholic”, with 10 of the Canadian Prime Ministers identified as such. (And are you surprised that Canada has only had Christian Prime Ministers?)
As simple as that, the category/value with the highest frequency is called the mode of the variable. Alternatively, you can easily spot the mode in a graph: it would be the largest slice of the pie or the tallest column in a bar chart or a histogram.
Do It! 3.1 Do all variables have a mode?
Considering that the only thing you need to do to find a variable’s mode is to count the frequency of each of its categories/values and indicate the one with the highest count, will it be possible to find the mode of any variable, regardless of its level of measurement? Or would the mode be a descriptive statistics applicable only to some variables depending on their level of measurement?
If by now you have a good grasp of what makes a variable nominal, ordinal, interval, or ratio (and if you do not — go back and really reread Section 1.3! (https://pressbooks.bccampus.ca/simplestats/chapter/1-3-levels-of-measurement/)), you should be able to easily answer the questions in the Do It! 3.1 above. Obtaining the mode, the simplest of all measures of central tendency, does not require any calculations or complicated procedures. To identify the mode, it doesn’t matter whether the categories of a variable are made of words or numbers, or if there is any order in them. All that matters is the count — the frequency — of responses in each category/value in order to identify where cases tend to cluster across the categories/values. As such, the mode is a descriptive statistic applicable to any and all variables.
To illustrate, let’s bring back the Example 2.2 (B) from Section 2.3:
Do It! 3.2 Educational Attainment’s Mode
Table 3.2 Educational Attainment
| Degree |
Count (a.k.a. frequency) |
| No degree | 1 |
| Secondary/High School | 6 |
| Associate’s | 3 |
| Bachelor’s | 5 |
| Master’s | 2 |
| PhD | 1 |
| Didn’t answer | 3 |
| TOTAL | 21 |
What is the mode for educational attainment based on the 21 respondents in the example?
Looking for the largest category in Table 3.2 above, you undoubtedly already identified that the mode for educational attainment is “Secondary/High School”. That is, to put this into language that even people non-trained in statistics could understand, the most frequent educational degree among the 21 respondents in the example is “Secondary/High School” as it has the highest frequency/the largest number of cases in it, 6. (It is generally quite useful to get into the habit of translating statistics-ese into English when you write reports so you should practice it on all occasions.)[1]
And this is all there is to finding out a variable’s mode. Beyond simply counting (applicable to groups of relatively small size, as generally no one would want to count hundreds or thousands of cases by hand), the ways to obtain a mode through SPSS are listed below.
SPSS Tip 3.1: Finding a Variable’s Mode
Option 1: Through a frequency table[2]
- Use SPSS to create a frequency table for your chosen variable[3];
- Look for the category/value with the highest frequency (the relative frequency in the Valid Percent column works too);
- Report the category with the highest frequency as the mode of that variable.
Option 2: Directly requesting the statistic
- From the Main Menu, select Analyze, then Descriptive Statistics, then Frequencies;
- Select your variable of choice from the left-hand side and use the arrow to move it to the right side of the window;
- Click on the Statistics button on the right;
- In the new window, check Mode in the Central Tendency section on your right;
- Click Continue, then OK.
Note that SPSS gives you the option to display a frequency table or not before clicking OK in the last step listed in the SPSS Tip above. The reason is practical: the frequency tables of interval/ratio variables can be quite long depending on the number of values they contain. As such, while identifying the mode from the frequency table of a nominal or ordinal variable is fine, it’s often more practical to request SPSS to report the mode of an interval/ratio variable directly rather than through a frequency table.
Watch Out!! #6… for Reporting Nominal/Ordinal Variable’s Modes As Given by SPSS
One thing to keep in mind when requesting the mode directly from SPSS is that SPSS will report modes by their number labels, or code (i.e., not by the actual name of the categories). If you recall from Section 2.1 (https://pressbooks.bccampus.ca/simplestats/chapter/2-1-data/), datasets contain only numbers, with nominal and ordinal categories appearing in code so that the software can work with them. As such, your SPSS output will list the mode of a nominal or ordinal variable as a number, and it is your job to “translate” that number into its proper form, i.e., its the actual category.
For example, in the Religious Affiliation of Canadian Prime Ministers example above, going in the order the categories are listed, the categories would typically be coded in the following way: “Anglican” =1, “Baptist” = 2, “Evangelical” = 3, “Presbyterian” = 4, “Roman Catholic” = 5, “United Church of Canada” = 6. The dataset would contain only the code (i.e., the numbers) and SPSS would report the mode as “5” in the output.
However, it is a mistake to report the code (the number label assigned to the category) instead of the actual category’s name. You should always report the mode with its real category name. (That is, it is up to you too look up the code — recall that you can do this through the Values column in SPSS’s Data View — and find the correct name of the modal category). In this case, you should report the mode of Religious Affiliation of Canadian Prime Ministers not as 5 but as “Roman Catholic”. (The “5” has no real meanings, it simply indicates that Roman Catholic is the fifth category in the listing.)
I’ll end this section with a final consideration regarding the mode: it is quite possible that a variable has more than one mode. After all, two (or more) categories/values might have the same frequency, so in that case we say that the variable’s distribution is multimodal (bi-modal or tri-modal in the specific cases of two or three modes). Depending on the number of modes, it’s acceptable to report only the first, while indicating that multiple modes exist for that variable. Multiple modes are usually also easy to spot in bar graphs and histograms: they appear as bars of equal height.
- Note that most frequent category does not mean that it contains the majority or most cases. Sometimes that may be the case, but it's not necessarily so. In both examples above you can see that neither Roman Catholics nor people with Secondary/High School degrees are a majority in their respective groups (10 out of 23 and 6 out of 21, respectively). Thus, be careful when writing about a mode as being "where most/the majority of cases cluster" because many times the phrasing would be factually incorrect. ↵
- You might want to avoid this option when working with interval/ratio variables, as their frequency tables can be very, very long. ↵
- See Section 2.3.4 (https://pressbooks.bccampus.ca/simplestats/chapter/2-3-4-what-frequency-tables-look-like/)for the tip on how to create frequency tables in SPSS. ↵