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# The Law of Averages

01:00 Tue 23rd Apr 2002 |

Q. So what is the difference between mean, median and mode

A. Cast your mind back to elementary statistics in maths and you may recall that there were various different methods of calculating an 'average', to whit: mean, median and mode.

Q. But surely an average is an average

A. In layman's terms, yes. An average is the generally prevailing rate or middle estimate or value of something. So, we use it to describe what might be termed 'normal'. However, in mathematics, more precision is required, and we get shades of average, the value of which can vary greatly even when using the same range of figures.

Q. How so

A. It depends on what exactly you are looking for. A few definitions might elucidate this somewhat.

Mean: Is the closest to what we understand as yer average average. Also known as the arithmetic mean, the formula to calculate the mean is sum of all the values in an arithmetical range divided by the number of items. The mean gives us an idea of the general size of the data without being too concerned with the actual details.

Median: The median is the exact middle of a range of values when arranged from smallest to largest. Statistically it is useful for allowing us to determine how many values in the range are above the median and how many below.

Mode: The mode is the item which occurs most frequently within any range of values.

A. OK. If your range of values...

(Q. Isn't there a statistical definition of 'range' as well

A. There is. The range tells you the difference between the smallest and largest value. But hang on...)

Q. Continue...

A. ...is:

2, 5, 9, 22, 55, 66, 77, 77, 125, 365

then your mean is: sum of items (803) divided by number of items (10), which equals 80.3

the median is: as we have 10 items in our range, the median will be the value between items 5 and 6, in this example 66 and 77; the median is thus 71.5 (it's easier if you have an odd number of items, because then you will have an actual figure to pick; so for example, the median of the range 1, 2, 3 is 2)

and the mode: the most frequently occurring value, that is 77

Q. And the range

A. The smallest value subtracted from the highest, so 365-2, which gives us 363.

Q. So, what is the Law of Averages

A. It is the law which states that an event will reoccur with a frequency roughly the same as its probability. So, if you toss a coin and it comes up tails four times in a row, then the Law of Averages states that it the probability is higher that it will land heads up next time. Which is, of course, false, as it has a 50:50 chance each and every time. And, as we all know, it is possible to fix the way a coin lands. If you have it heads-up on your thumb, spin it, catch it in your hand and turn it over on to the back of your other hand, more often than not it will be heads. It works, honest...