Often, the purpose of statistics is not just to show quantitative data, but also to present easily interpretable information or estimate. Saying “one in five” instead of “500 out of 2500 people” makes a huge difference in the way we perceive data. We often express big numbers by scaling them down to reasonable limits. The most common way to do this is by using percentages. Percentages (per 100) suffice in most practical situations.
However, there are situations where 100 is too big or too small a number to express a statistic accurately. For example, in a situation where we are dealing with the statistic “8 students out of 40”, imagine saying “20%” and “1 in every 5 students”. Both are correct, but certainly, the second is a more user-friendly way of presenting it, meant for easier interpretation.
The basic idea behind selecting a particular value of x in the expression “per x”, is to have a reasonably long range for possible values of that piece of data, preferably whole numbers, as you will see in examples below. This enables us to do justice to data while making estimates.
- Imagine the rate of something that typically lies only between 1% and 2% (e.g. birth rates and death rates). It would not be fine for us to estimate 1.2% as 1% in this case; it gives convenient data, but it kills information. So, we would choose a much larger value for x; for x = 1000, the range would become 10 to 20, and this particular value would be 12. We wouldn’t need to round off 12 to 10, because it’s a whole number.
- Now imagine the rate of something that typically lies between 50% and 90% (e.g. literacy rates). Here, a figure 62.3% can be rounded off to 62% without much trouble. 62.3% gives as much information as 62% in this particular context. Since the range is big, it gives convenient data as well as reasonably accurate information. So, we prefer to keep the value of x at 100, and not use “per 1000”.
Also worth mention here is sex ratio. Sex ratios are often expressed as “x females per 1000 males”. We don’t use percentages here, because the whole point of expressing in different ways is to make statistical data useful information in practical life.
And obviously, we choose multiples of 10 so as to make it easier to interpret and calculate. So after 100, the next possible choice is 1000.