# IQ scales – how do they work? (Part I)

Intelligence Quotient (IQ) scales have changed over time. When IQ tests were invented by Frenchman Alfred Binet in the late 1800s. IQ scores at that time were based on the very simple concept of Mental Age (MA) and Calendar Age (CA). In fact, the origin of the term Intelligence Quotient lies in the calculation of the intelligence score which was calculated as someone’s Mental Age divided by that person’s Calendar Age. Expressed mathematically, we get the following quotient:

IQ = (MA / CA) x 100

The multiplication of the score by 100 would help facilitate the interpretation of the IQ scale in that the score is an integer rather than being a fraction. But let me park this point for a few moments.

What can be clearly seen from this IQ equation is that if MA = CA, then the IQ score will be 1 x 100 = 100. If MA on the other hand exceeds the denominator of the equation, the IQ score will exceed 100, while if the MA is lower than the CA, then that person’s IQ score will be less than 100. It’s as simple as that.

So what does this mean in plain English? This means that under the old method of calculating IQ, a person with a Mental Age is excess of his years, will have an IQ which is greater than 100. If on the other hand, that person’s Mental Age is less than that person’s Calendar Age, than this person will have an IQ of less than 100. And yes, you’ve guessed it, if CA and MA are equal, than this person will have an IQ of 100. Binet’s equation was beautifully simple, and establish someone’s Calendar Age is simple enough (you establish their birthday and then you can calculate age!), but how does one go about establishing what a person’s MA should be?

### IQ scales – it first started with establishing an MA scale

This is where the concept of IQ scales come in. More specifically, Binet had to establish an MA scale for each population of children of a certain age. That is, in establishing an IQ scale, Binet first had to determine how each age group would perform on specific mental tasks that were believed to be relevant to the idea of cognitive function. So Binet would have needed to establish a series of tasks and would have needed to see how ‘far’ children of a given age would have gotten on these tasks, and made a determination as to what the average expectation was for each age group.

I will leave you to digest the points that I have made so far: (1) Binet invented the IQ test in the late 1800s; (2) he proposed a beautifully simplistic formula cor calculating IQ = MA / CA x100; (3) establishing CA is simple, but MA requires having a scale for each age group. This involved testing a large sample of children of particular age groups to establish what the average performance at every age should be. In my next posting, I will explain why although beautifully simplistic, this Intelligence Quotient method would end up breaking down and would be superseded by standard scores. In the meantime, you can try our IQ test here.