Fill in the points of every team of the following classification of the teams of the League of the Spanish soccer:
Team 
Points 
Barcelona 

Real Madrid 

Seville 

Valencia 

Villareal 

Atlético 

Malaga 

Deportivo 

Majorca 

Almeria 

Athletic 

Racing 

Betis 

Osasuna 

Getafe 

Sporting 

Recreativo 

Valladolid 

Espanyol 

Numantia 


Find the median of the points of the teams.

Find the median of the points of the teams in positions to play European competitions the following year (the first six teams in the table).
 Find the median of the teams in relegation position (the last three teams in the table).
Development:
We define the following scorings.
Team 
Points 
Barcelona 
81 
Real Madrid 
75 
Seville 
63 
Valencia 
56 
Villareal 
56 
Athletic 
54 
Malaga 
53 
Deportivo 
53 
Majorca 
53 
Almeria 
51 
Athletic 
50 
Racing 
41 
Betis 
40 
Osasuna 
40 
Getafe 
33 
Sporting 
33 
Recreativo 
33 
Valladolid 
29 
Espanyol 
28 
Numantia 
28 
 Bearing in mind that $$20$$ teams are taking part, there will be two central values. Since it is an arranged classification, it is not necessary to do a table of cumulative frequencies. It is enough to at the scorings of the teams in positions $$10$$th and $$11$$th.
Almeria  $$51$$ points
Athletic  $$50$$ points
And so, the median will be the average of $$50$$ and $$51$$: $$50,5$$ points.
 As there are $$6$$ teams in position to play in Europe the next year, we divide both points of the third and fourth team.
$$$\dfrac{63+56}{2}=59,5$$$
The median is $$59,5$$ points.
 The median will be the value of the scoring of the team in the intermediate position of those who are in relegation (that is, the scoring of the Espanyol).
And so, the median of the teams in relegation is $$28$$ points.
Solution:
Team 
Points 
Barcelona 
81 
Real Madrid 
75 
Seville 
63 
Valencia 
56 
Villareal 
56 
Athletic 
54 
Malaga 
53 
Deportivo 
53 
Majorca 
53 
Almeria 
51 
Athletic 
50 
Racing 
41 
Betis 
40 
Osasuna 
40 
Getafe 
33 
Sporting 
33 
Recreational 
33 
Valladolid 
29 
Espanyol 
28 
Numantia 
28 
 Mode = $$50,5$$ points
 Mode = $$59,5$$ points
 Mode = $$28$$ points