In the study of Statistic, at central tendency measures they are an excellent tool for reducing a set of values into one. Among the measures of central tendency, we can highlight the arithmetic average, average weighted arithmetic, a fashion and the median. In this text, we will address the average.
The term "median" refers to "quite". Given a set of numerical information, the central value corresponds to the median of that set. As such, it is important that these values are placed in order, either ascending or descending. If there is a quantity odd of numerical values, the median will be the central value of the numerical set. If the amount of values is a number pair, we must make an arithmetic mean of the two central numbers, and this result will be the value of the median.
Let's look at some examples to better clarify what median is.
Example 1:
João sells popsicles in his house. He recorded the amount of popsicles sold in ten days in the table below:
Days |
Quantity of popsicles sold |
1st day |
15 |
2nd day |
10 |
3rd day |
12 |
4th day |
20 |
5th day |
14 |
6th day |
13 |
7th day |
18 |
8th day |
14 |
9th day |
15 |
10th day |
19 |
If we want to identify the average of the amount of popsicles sold, we must order this data, placing them in ascending order, as follows:
10 |
12 |
13 |
14 |
14 |
15 |
15 |
18 |
19 |
20 |
Since we have ten values, and ten is an even number, we must make an arithmetic mean between the two central values, in this case, 14 and 15. Let M.A be the arithmetic mean, then we will have:
M.A. = 14 + 15
2
M.A. = 29
2
M.A. = 14.5
The median amount of popsicles sold is 14,5.
Do not stop now... There's more after the advertising ;)
Example 2:
A television program recorded the ratings achieved over the course of a week. The data are registered in the table below:
Days |
Court hearing |
Monday |
19 points |
Tuesday |
18 points |
Wednesday |
12 points |
Thursday |
20 points |
Friday |
17 points |
Saturday |
21 points |
Sunday |
15 points |
To identify the average, it is important to order the audience values in ascending order:
12 |
15 |
17 |
18 |
19 |
20 |
21 |
In this case, since there are seven values in the numerical set, and seven is an odd number, no calculation is necessary, the median is exactly the central value, ie, 18.
Example 3: In one school, the ages of a group of 9th graders were recorded according to sex. From the values obtained, the following tables were formed:
Girls |
15 |
13 |
14 |
15 |
16 |
14 |
15 |
15 |
boys |
15 |
16 |
15 |
15 |
14 |
13 |
15 |
16 |
14 |
15 |
14 |
Let's find the girls' median age first. For this, let's order the ages:
13 |
14 |
14 |
15 |
15 |
15 |
15 |
16 |
There are two core values and both are “15”. The arithmetic mean between two equal values is always the same value, but to leave no room for doubt, let's calculate the arithmetic mean:
M.A. = 15 + 15
2
M.A. = 30
2
M.A. = 15
As previously mentioned, the median age of girls is 15. Let's now find the median age of the boys, putting the ages in ascending order.
13 |
14 |
14 |
14 |
15 |
15 |
15 |
15 |
15 |
16 |
16 |
As we have only one central value, we can conclude that the median age of boys is also 15.
By Amanda Gonçalves
Graduated in Mathematics
Would you like to reference this text in a school or academic work? Look:
RIBEIRO, Amanda Gonçalves. "Median"; Brazil School. Available in: https://brasilescola.uol.com.br/matematica/mediana.htm. Accessed on June 27, 2021.
