Centrality measures are real numbers used to represent whole lists of data. In other words, when analyzing a quantity, we can gather numerical data about it and put it in a list. For various reasons, it may be necessary to represent this entire list with a single value, which is precisely a centrality measure.
Example:
In a survey, data from 100,000 Brazilians are recorded and, based on the information obtained from it, it is possible to conclude that Brazilians have a life expectancy of 73.6 years. This does not mean that every Brazilian lives a little over 73 years old, but it does mean that, average, this is the Brazilian's lifetime. If we look for the complete survey data, we will notice that some Brazilians die at birth and others over 100 years of age.
Now why not just look at the completed surveys? Approximately half a century ago the Brazilian's life expectancy was just 55 years. This indicates that there have been significant advances in quality of life, medicine and care for the elderly since then. Therefore, many
Dice can be extracted from a centrality measure without having to analyze all the information of 100,000 people one by one.At centrality measures most important for Elementary and High School are:
→ Fashion
Fashion is the number that is most repeated in a list. To get the fashion, therefore, just look at the number that repeats the most and it will be the fashion. Heads up: it is not the number of repetitions, but the number that is repeated.
Example: From the ages of the sixth graders in the list below, determine the fashion.
12 years, 13 years, 12 years, 11 years, 11 years, 10 years, 12 years, 11 years, 11 years
Note that there are 9 students in total, 4 of whom are 11 years old and 3 are 12 years old. So the mode of this list is 11.
It is worth mentioning that:
A list that has two items that are repeated the most is called bimodal and has two fashions;
A list that has three or more items that are repeated the most is called a multimodal.
→ median
Arranging a list of numbers in ascending or descending order, the value that appears exactly in the middle of the list is the average.
Example: The following list is made up of the grades of some elementary school students from school Z. Determine the median of this list.
Student A - 2.0
Student B - 3.0
Student C - 4.0
Student D - 4.0
Student E - 1.0
Student F - 2.0
Student G - 5.0
Note that the list is not in order. Ordering it, we have:
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1,0; 2,0; 2,0; 3,0; 4,0; 4,0; 5,0
The value that appears in the center of this list is 3.0. So this is the average of the grades of students from school Z.
There is also the possibility that the list has an even number of information. In this case, take the two numbers that appear in the center, add them up and divide them by 2. Watch:
At school Z, some elementary school students took the following grades. calculate the average of these notes.
Student A - 2.0
Student B - 3.0
Student C - 4.0
Student D - 4.0
Student E - 1.0
Student F - 2.0
Arranging the list in ascending order, we have:
1,0; 2,0; 2,0; 3,0; 4,0; 4,0
The two most center values are 2.0 and 3.0. Adding them and dividing them by 2, we have:
2,0 + 3,0 = 5,0 = 2,5
2 2
Therefore, the average é 2,5.
→ Arithmetic average
The arithmetic mean is also known as average value and is obtained by the sum of the no data from a list and dividing that result by no. In other words, add up all the numbers and divide the result by the number of pieces of information that were added.
Example: Knowing that it is calculated by arithmetic average, what is the final grade of a student who has the following averages:
1st Bimester: 7.0
2nd Bimester: 5.0
3rd Bimester: 4.0
4th Bimester: 9.0
Follow the procedure suggested above:
7,0 + 5,0 + 4,0 + 9,0 = 25 = 6,25
4 4
→ weighted average
It's the same arithmetic average, however, we consider that some values appear more than once or have Weight different from others.
Example: Teachers often want the final test to have a higher value than the first, so they say that the weight of the first test is 1 and the second is 2. In other words, the second test is worth twice the first.
To calculate the weighted average, multiply each data by its respective weight, add the results of these products and, finally, divide the value obtained in this last step by the sum of the weights.
Example:
From the previous example, calculate the student's grade if the weights were:
1st Bimester: 1
2nd Bimester: 3
3rd Bimester: 3
4th Bimester: 1
Multiply the grades by the weights and divide the result by the sum of the weights:
1·7,0 + 3·5,0 + 3·4,0 + 1·9,0 = 43 = 5,37
1 + 3 + 3 + 1 8
By Luiz Paulo Moreira
Graduated in Mathematics
