Median statistics: concept, properties and calculation

In order to have an idea about this or that phenomenon, we often use averages.They are used to compare the level of wages in various industries, temperature and rainfall in the same area in the same period of time, the yield of crops in different geographical areas, and so on. D. However, the average is not the only general indicator- In some cases, a more accurate assessment approaches such as the value of the median.In statistics, it is widely used as an auxiliary descriptive distribution characteristics of a feature in a particular population.Let's see how it differs from the average, as well as what caused the need for its use.

median statistics: definition and properties

Imagine the following situation: the firm together with the director employs 10 people.Ordinary workers receive 1000 USD., And their leader, who, besides, is the owner, - 10000 UAH.If we calculate the arithmetic mean, it turns out that the average salary in the enterprise is equal to 1900 UAH.Is this statement true?Or take an example, in the same hospital ward is nine people at a temperature of 36,6 ° C, and one person with whom she is 41 ° C.Arithmetic mean in this case is (36.6 * 9 + 41) / 10 = 37,04 ° C.But this does not mean that every one present ill.All this suggests the idea that one medium is often not enough, and that is why, in addition to its use median.In statistics, this indicator is called the option that is right in the middle of an ordered series of variations.If we calculate it for our examples, we get 1000 UAH respectively.and 36,6 ° C.In other words, a median in statistics is a value that divides the number in half so that on both sides of it (up or down) is arranged the same number of units of a given population.Because of this property, this indicator has a few names: 50th percentile or quantile 0.5.

How to find the median in the statistics

method of calculation of this value depends on what type of variational series we have: a discrete or interval.In the first case, the median in the statistics is quite simple.All you need to do is to find the sum of the frequencies, divide it by 2 and then add to the result of ½.It is best to explain the principle is based on the following example.Suppose we have grouped data on fertility and want to find out what is the median.

After some simple calculations, we find that the desired figure is: 195/2 + ½ = 98, ie,98th version.In order to find out what it means to be consistently accumulate frequency, beginning with the smallest variations.Thus, the sum of the first two lines gives us 30. It is clear that there are 98 options.But if we add to the result of the frequency of the third option (70), we obtain a sum equal to 100. It is just 98-I variant, so the median is the family that has two children.As for the interval number, there is usually used the following formula:

HMe + Me = iMe * (Σf / 2 - SMe-1) / fMe in which:

• HMe - the first value of the median interval;
• Σf - the number of (the sum of the frequencies);
• iMe - the median value of the range;
• fMe - median frequency range;
• SMe-1 - the sum of cumulative frequencies in the range preceding the median.

Again, without an example here is quite difficult to understand.Suppose we have data on the value of wages.

To usethe above formula, we first need to determine the median interval.As such the range is selected, the cumulative frequency is greater than half the sum frequency or is equal to it.So 510 divided by 2, we see that this criterion corresponds with the value of the salary range of 250,000 rubles.up to 300,000 rubles.Now you can expose all the data in the formula:

+ Me = HMe iMe * (Σf / 2 - SMe-1) / fMe = 250 +50 * (510/2 - 170) / 115 = 286.96 thousand. Rub.

We hope our article has been helpful, and now you have a clear idea of ​​what the median in the statistics and how it should be calculated.