Very often in conversations with friends and acquaintances the following questions are asked:
“How many thousand kilometers a year do you drive your car on average?”
“What is your average monthly electricity bill?”
“How much money do you spend on average a month for medicines?”
Life itself has required us to search for averages, and why will we try to show you one specific case to make it clearer.
The example would be from the energy sector – central heating or electricity heating.
On September 1, an increase in the price of heating by 11% was announced and you are in a dilemma – to stop it and use electric heating or leave it. The benefits and harms to health will not be the case, but the purely mathematical (financial) side of the issue.
The downstairs neighbor has kindly provided you with his electricity bills, and he has long ago made his choice in favor of electricity. Let’s look at the data first of the neighbor’s bills:
And now your costs, and we’ll add the ones for electricity:
Based on this example, we will try to explain the notion of statistics in the average value, which in order to be more interesting can be calculated in several different ways, another question is which one is best for you.
And so the most widespread and easiest to calculate is the MEAN method, where we simply collect all the values and divide them by the number of collectables – in this case 12 months.
For the neighbor 82 + 75 + 70 + 52 + 40 + 41 + 42 + 13 + 42 + 54 + 74 + 80 = 665
665/12 = 55.40 average monthly electricity bill.
And yours: 88 + 83 + 88 + 48 + 21 + 22 + 45 + 55 + 20 + 56 + 85 + 89 = 700
700/12 = 58.30 average monthly electricity and heating bill.
The conclusion seems clear even without the intended increase in the price of steam heating.
Wondering why there are other ways to calculate? Each of them will give a different perspective on the numbers and depending on the question you are trying to answer, each of the three may be the most appropriate.
But as you can see in your neighbor’s data and yours there are either very low or very high values, the reasons may be different, but the result is there. Your neighbor felt cool in his cottage in August, while you turned on the air conditioning in the heat.
For this reason, statistics also offer another method of determining the average value – the MEDIANA method. Given the word itself is of medium importance. However, for this purpose, the data must be in ascending or descending order and the average in the series is the average. In this case we have an even amount of data, in which case we resort to their mean value. Let’s write it down:
82 75 70 52 40 41 42 13 42 54 74 80 and arrange them in ascending order
13 40 41 42 42 52 54 70 74 75 80 82, where 52 and 54 are the averages and their arithmetic mean is 53 which is the MEDIANA (the average value of the neighbor’s electricity bill).
Now yours too:
88 83 88 48 21 22 45 55 20 56 85 89 or in ascending order
20 21 22 45 48 55 56 83 85 88 88 89, where 55 and 56 are the averages and 55.5 is the MEDIANA (the average of your bill).
From a real point of view, the data calculated using this method is less than the mean one, but there is another thing to consider – the longer the data series are, for example, you included two last year bills, when you were not in the hot months home and your neighbor was home watching some football championships, the differences between the mean and the median would get smaller.
There is also a third way of calculating the average value called MODE – to be honest, firstly it is the least used method and secondly the result is highly dependent on side factors, but still to mention it – just look at the numbers that most often appear in the database . There is a possibility that there may be more than one mode or no mode, which makes it difficult to determine the average.
In this series of data there is another important parameter. And this is the range of values. The average value is naturally an interesting parameter, but in countries with a pronounced continental climate, where winters are cold and summers are hot and we want to live in normal temperatures (the air conditioner works both in winter and in summer). Purely mathematically, the range is the difference between the largest and the smallest value, often confused with the largest and smallest value, but this is not correct.
So your neighbor is 82-13 = 69 and you are 89-22 = 67. The range shows the breadth of the data, how far the values from the lowest to the highest data are.