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Mode: an alternative average is called the ‘mode’. Mode means ‘fashionable’, which describes very well just what the statistical mode is. It is simply the value in any set of scores that occurs most often – or is the most ‘popular’. Take the following set of numbers: 5, 6, 7, 8, 8, 8, 9, 10, 10, 12. As the number 8 occurs most often (three times), 8 is the mode of these set of numbers. If one of the 8s vanished, we would be left with two 8s and two 10s. In this case, there would be two modes of values 8 and 10 and this is known as bimodal. An example of a bimodal distribution is the height of six children in a nursery all aged 2 years. They are 40, 40, 40, 40, 80, 80, 80. Although the mean is 60, this figure is not a good indication of the height of any single child in the nursery aged 2 years. We would be far better off knowing that there are two modes of values 40 and 80.
If on the other hand the numbers were 5, 6, 7, 8, 9, 10, in which there is no single number that occurs more than once, there is no mode as all the numbers appear with the same frequency.
Advantages of the mode:
The mode can be a very useful statistic. One of its main assets is that it can be used to indicate a ‘normal’ or ‘usual’ figure. It is exactly opposite to the mean in this respect, as the modal value must be a commonly occurring figure. Often the value of a mean is a number with a decimal point, and sometimes may not remotely resemble and of the values in the data set – as in the nursery children. Often people use the mode as an average as in the ‘average person’, the figure quoted being the usual or typical value, and quite often will not be the mean.
The mode is also a useful descriptive statistic when the numbers in a distribution are not evenly a spread around a central value (as is the median). Such a lopsided distribution is called a ‘skewed’ distribution.
Disadvantages of the mode are however:
Firstly and sadly, the mode is hardly ever used, due to its instability as it can swing wildly through the whole set of numbers at the drop of a hat. Take the numbers 1, 1, 6, 7, 8, 10. The mode here is 1, which is not a very representative figure of the group as a whole. However if we change the score of 1 to a 10, the mode shifts right to the other end of the scale. Thus a single number change can alter the mode dramatically. This is in great contrast to the mean (average) and the medium, where number changes can take place and leave them virtually unaffected.
If a distribution of numbers has more than two modes, and with large sets of numbers, it might be possible to have many modes – then the modal values themselves could need summarising, and so the usefulness of the mode as a descriptive statistic begins to dwindle.
Measures of Dispersion
Another type of descriptive statistic is used to qualify the word about as in the sentence ‘on average about 600 cans of Pedigree Chum are bought each week from the supermarket’ – in the section on averages (means). As we have already established over a four-week research period, there were between 535 and 692 cans of Pedigree Chum sold. If there were 440 cans of Pal (another type of dog food) sold in the first week, 589 sold in the second week, 670 sold in the third week and 701 sold in the fourth week, the average number of cans of Pal sold over the period would also be 600.
However, the word about signifies that there may be, and are, large departures of actual cans sold from the averages for each type of dog food. Used by itself, the word about is far too vague, and we need some means of giving more details about the variation. The solution is to use one of the descriptive statistic known as the measure of spread; these simply indicate just how much the word ‘about’ means for a particular set of figures, and indicates how widely scattered the numbers are. If one of these measures is used together with one of the averages, then the two summary numbers together will give an extremely concise and useful description of the particular distribution. There are three commonly used measures of dispersion (see below).
The range tells you over how many numbers altogether a distribution is spread. It is easily obtained by subtracting the smallest score from the largest. For example, if I found that various kinds of potatoes for sale in several greengrocers’ shops were priced at 10p, 25p, 12p, 8p, 14p, 14p, 14p 24p and 15p per lb, the range for these prices would be 25p-8p = 17p.
The problem with the range is that extreme value have a very big effect on the descriptive statistic and outliers (atypical extreme values) may cause distributions which overall look very different to have similar ranges. Clearly then, the range can only be used sensibly as a descriptive statistic when all the scores are fairly well bunched together.