What is the median and how to calculate it
Miscellaneous / / December 09, 2021
Let's interpret the statistics correctly.
What is the mean and why is it not always correct
When we deal with statistical data, they need to be structured somehow. By themselves, demographics and economics, such as wages and life expectancy, grades, scores, and more, are just a jumble of numbers.
To bring them to order, you can use the mean arithmetic meaning. To do this, you need to foldMean, median, and mode review / Khan Academy all numbers and divided by the number of terms:
(8+7+10+4+6+9)/6=7,3
And although the arithmetic mean is easy to calculate, it has a serious drawback: if one indicator is very different from the others, then it seriously distorts the final result. The situation is well described by an anecdote: “Officials eat meat, and I eat cabbage. On average, we eat cabbage rolls. "
The arithmetic mean can be significantly larger or smaller than most numbers. So, in the row "1, 2, 1, 1, 3, 8, 10, 1, 587" it will be equal to 68.2. And if nine people with savings of 100 thousand rubles and one bankrupt with half a million debt are included in the total calculation, the average amount of savings will be 40 thousand.
Simply put, the arithmetic mean may not reflect reality.
What is the median and how is it better
To insure against such errors, instead of the average value, you can useCalculating the median / Statistics Canada median.
The median will help you find exactly the indicator that is closest to the true average. It is not affected by numbers that are out of the total mass, therefore it is considered one of the most reliable and stable indicators. So, for the above series "1, 2, 1, 1, 3, 8, 10, 1, 587" the median will be 2. If you put 87 instead of 587, it will still be equal to 2, if 7 - also 2. The arithmetic mean in similar cases will change: 12.7 and 3.8, respectively.
Using the median, you can get more accurate data and better interpret statistics. For example, when calculating the average wages, when 19 employees receive 20 thousand rubles each, and the director - a million. The arithmetic mean in this case will be equal to 69 thousand rubles, and the median is 20. Therefore, the latter is preferred by people working with numbers: from accountants to scientists.
The median value is calculatedMean, median, and mode review / Khan Academy from a number or a pair of numbers that are more than one half of the indicators and less than the other. To find the median, you need to arrange the set of numbers and just find the middle in it. Like this: “1, 1, 1, 1, 2, 3, 8, 10, 587».
If the series has an even number of indicators, such as in “1, 1, 1, 1, 2, 3, 8, 10 ", you need to take two middle numbers. These are 1 and 2. They need to be added, and the amount must be divided in half:
(1+2)/2=1,5
How to calculate the median when there is a lot of data
In this case, you can use special tools.
Online
For example, on the site Calculator Soup. It is enough to copy the data into the required window and click on the "Calculate" button. In addition to the median, the calculator will immediately calculate a bunch of other things: the arithmetic average, the minimum and maximum values, the number of indicators, the total amount, and so on.
Excel
The table editor has a "Median" function. It is enough to find it in a special window and select an array of data to calculate the indicator. The same can be done in Google docs.
Are there alternatives to the median
Sometimes you may need to find not the maximum average indicator, but the most frequent one. For example, when you need to figure out the most popular size in a clothing store. In this case, you need to use fashion. This is the meaning that occursMean, median, and mode review / Khan Academy more often than others. So, in the row "1, 2, 1, 1, 3, 8, 10, 1, 87", fashion is 1. Several numbers can be a fashion at once. Like the median, it can be calculated using an online calculator and Excel.
In addition to the median, percentiles, quantiles, and quartiles can be used. They are needed for more complex calculations. For example, to calculate how many percent of people in the country earn 50 thousand rubles or less. Indicators divide the data into equal parts: percentiles - by 100, quantiles - by 10, quartiles - by four. For example, the median is the 50th percentile or second quartile.
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