Mean, median, mode: does an understanding of these statistical terms count as Universal Knowledge? Can most adults be expected to know the difference, and why you would use one statistical measurement rather than another? In my experience, probably not. We can conclude that plenty of people are unfamiliar with basic statistics because the word “average” has come to mean “not very good”.

Anyone who understands statistics at a basic level will know that the phrase “Half of all hospitals are below average” is, simply, mathematically correct. Half of anything that you can measure will be below average and the other half will be above average (although some instances might be bang in the middle: average). For people who don’t understand statistics the phrase “Half of all hospitals are below average” sounds bad. Half of all schools are below average too. That’s just the way it is.

Mean, median and mode are the three ways of working out an average, though the word “average” usually implies “the mean”. At school (where I studied Maths to A-Level, and got an A, so I used to know something about this) we spent plenty of time working out the mean for a dataset. (“Dataset” here means a set of numbers.) A simple example would be scores in a spelling test. For example, 10 children each have to spell 10 different words. Add up all the correct answers and divide by the number of children (10 in this example) and you have the average (or mean) score. If the total number of correct answers is 72 then the mean score per child is 7.2. In this case every child’s score will either be above average or below average. (Nobody can score exactly 7.2 in this spelling test.)

The median is the value exactly in the middle of a dataset arranged in numerical order. For example, if you could arrange all 7.4 billion people in the world in order of age, the person in the very middle of that very long line would be 27. If you are 28 or older you are in the older half of the world’s population. This figure came as a surprise to me. I looked it up a few years ago when my son asked, “Are there more people in the world who are younger than you or older than you?” I figured I was already in the older half of the global population but now find that I would be in the older half of the male population in any country in the world. Even Monaco, at the top of the list, has a median age for men of 50.6. In Uganda, though, anyone aged 16 or older is already in the older half of that country’s population. The Median age for men is 15.6, and it’s only 15.7 for women (usually the gap between median ages for women and men is much greater than 0.1 of a year). If you want to check the values for other countries, follow this link to the CIA website (yes, that CIA). And if you want to see how the world’s population is increasing check out the world population clock at worldometers.com, here.

Mode, the third way of calculating the “average”, gives the value that occurs most often in a dataset. It could be a more useful way of calculating the average number of children per family than the much-derided “2.4 children”. (I have heard enough people kvetching along the lines of “Whoever heard of point four of a child”, and would prefer never to hear it again.) In the UK it’s more like 1.7 or 1.8 children per family now, but according to the latest information from the Office for National Statistics here in the UK, among families with dependent children, 1 child in now the most common number in the UK. As the survey says:

In 2015 45% of families with dependent children had only 1 dependent child in the family at the time of the survey, this is the same percentage as in 2005. In 2015, 40% of families with dependent children had 2 dependent children.

This BBC page from 2007 claims that “two children remains the most common family size” but if we’re looking at dependent children the ONS suggests that the most common family size has been one child for well over ten years.

The most memorable thing that I have read recently involving a mode calculation (and the reason why I have been thinking about mean, median and mode) is about the mode age of death. Until 1964 the mode age of death in the UK was zero. This meant that the number children dying before their first birthday was greater than the number of people dying at any other age. This was probably true for every previous year that there have been people in these islands. 1964 was the last year for which that was true. In 2013 the mode age of death was 87. This all represents enormous progress in healthcare, for everyone from zero to 80-odd. In “the least developed parts of the world” though (to quote from this short BBC article) the mode of age of death is still zero: in those countries, in 2012, 1 in 17 children died before their first birthday. This still indicates big progress (in 1990 the figure was 1 in 9 children) but those of us in “the developed world” with children can be grateful that there has never been a safer time to be born or to grow old.