{"id":68,"date":"2018-10-31T17:14:21","date_gmt":"2018-10-31T21:14:21","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/simplestats\/?post_type=chapter&p=68"},"modified":"2019-08-09T19:11:24","modified_gmt":"2019-08-09T23:11:24","slug":"3-1-mode","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/simplestats\/chapter\/3-1-mode\/","title":{"raw":"3.1 Mode","rendered":"3.1 Mode"},"content":{"raw":" \r\n\r\nCentral 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.\r\n\r\n \r\n\r\nThere are three measures of central tendency: mode, median, and mean<\/strong>. In this section, we explore the mode.<\/em>\r\n\r\n \r\n\r\nTo 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<\/em> column will do you just as well). Here is a simple, small-N<\/em>, real-world example.\r\n\r\n \r\n
\r\n

Example 3.1 Religious Affiliation of Canadian Prime Ministers<\/em><\/p>\r\n\r\n<\/header>\r\n

\r\n\r\nTable 3.1 Religious Affiliation of Canadian Prime Ministers (Wikipedia 2017)<\/em>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Religious affiliation<\/strong><\/td>\r\nFrequency<\/strong><\/td>\r\n<\/tr>\r\n
Anglican<\/td>\r\n4<\/td>\r\n<\/tr>\r\n
Baptist<\/td>\r\n3<\/td>\r\n<\/tr>\r\n
Evangelical<\/td>\r\n1<\/td>\r\n<\/tr>\r\n
Presbyterian<\/td>\r\n3<\/td>\r\n<\/tr>\r\n
Roman Catholic<\/td>\r\n10<\/td>\r\n<\/tr>\r\n
United Church of Canada (prev. Methodist)<\/td>\r\n2<\/td>\r\n<\/tr>\r\n
TOTAL<\/td>\r\n23<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n \r\n\r\nWhat 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?\r\n\r\n \r\n\r\nSurprising 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.,\u00a0the category with the highest frequency<\/strong> -- 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?)\r\n\r\n<\/div>\r\n<\/div>\r\n \r\n\r\nAs simple as that, the category\/value with the highest frequency is called the mode of the variable<\/strong>. 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.\r\n\r\n \r\n
\r\n

Do It!<\/em> 3.1\u00a0 Do all variables have a mode?<\/em><\/p>\r\n\r\n<\/header>\r\n

\r\n\r\nConsidering 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?\r\n\r\n<\/div>\r\n<\/div>\r\n \r\n\r\nIf 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<\/em> 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<\/em> or numbers<\/em>, or if there is any order in them. All that matters is the count<\/em> -- the frequency -- of responses in each category\/value in order to identify where<\/em> cases tend to cluster<\/em> across the categories\/values. As such, the mode is\u00a0a descriptive statistic applicable to any and all variables<\/strong>.\r\n\r\n \r\n\r\nTo illustrate, let's bring back the Example 2.2 (B) from Section 2.3:\r\n
\r\n

Do It! 3.2\u00a0 <\/em>Educational Attainment's Mode<\/em><\/p>\r\n\r\n<\/header>\r\n

\r\n\r\nTable 3.2 Educational Attainment\u00a0<\/em>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Degree<\/strong><\/td>\r\n\r\n

\u00a0Count (a.k.a. frequency<\/em>)<\/strong><\/p>\r\n<\/td>\r\n<\/tr>\r\n

\u00a0 \u00a0No degree<\/td>\r\n1<\/td>\r\n<\/tr>\r\n
\u00a0 \u00a0Secondary\/High School<\/td>\r\n6<\/td>\r\n<\/tr>\r\n
\u00a0 \u00a0Associate's<\/td>\r\n3<\/td>\r\n<\/tr>\r\n
\u00a0 \u00a0Bachelor's<\/td>\r\n5<\/td>\r\n<\/tr>\r\n
\u00a0 \u00a0Master's<\/td>\r\n2<\/td>\r\n<\/tr>\r\n
\u00a0 \u00a0PhD<\/td>\r\n1<\/td>\r\n<\/tr>\r\n
\u00a0 \u00a0Didn't answer<\/td>\r\n3<\/td>\r\n<\/tr>\r\n
\u00a0 \u00a0TOTAL<\/strong><\/td>\r\n21<\/strong><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nWhat is the mode for educational attainment based on the 21 respondents in the example?\r\n\r\n<\/div>\r\n<\/div>\r\n \r\n\r\nLooking for the largest category in Table 3.2 above, you undoubtedly already identified that the mode for educational attainment<\/em> 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<\/em> into English when you write reports so you should practice it on all occasions.)[footnote]Note that most frequent<\/em>\u00a0category does not mean that it contains the\u00a0majority<\/em> or most<\/em> 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<\/em>\u00a0of cases cluster\" because many times the phrasing would be factually incorrect. [\/footnote]\r\n\r\n \r\n\r\nAnd 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.\r\n\r\n \r\n
\r\n

SPSS Tip 3.1: Finding a Variable's Mode<\/em><\/p>\r\n\r\n<\/header>\r\n

\r\n\r\nOption 1: Through a frequency table<\/strong>[footnote]You might want to avoid this option when working with interval\/ratio variables, as their frequency tables can be very, very long.[\/footnote]\r\n