Question

In the $2010$ football World Cup, Spain won and Brazil was knocked out in the quarter finals. The number of goals they scored in their matches are shown below. Work out the mean score and state which team scored more goals per match, overall.

Answer 1

Hint:We are provided with the number of goals that teams scored in the individual matches. To find out which team scored more goals per match we need to find out the average goals per match for the both teams. For finding average goals per match we need to add all the goals that team scored individually and divide with total number of matches they played and compare the average goals per match of both to get the required answer.

Complete step-by-step answer:
Let us note down the goals by Spain.
Goals by Spain in the continuous matches are $0$,$2$,$2$,$1$,$1$,$1$ and $1$.
The number of matches that Spain played $ = 7$
Let us calculate the total number of goals that Spain scored $ = 0 + 2 + 2 + 1 + 1 + 1 + 1 = 8$
Let us note down the goals by Brazil.
Goals by Brazil in the continuous matches are $2$,$3$, $0$, $3$ and $1$
The number of matches that Brazil played $ = 5$
The number of matches for Brazil is low because it is knocked out in the quarter finals whereas Spain won the finals.
Let us calculate the total number of goals that Brazil scored $ = 2 + 3 + 0 + 3 + 1 = 9$
Now, let us find which team scored more goals per match. To find that we need to find the means of the goals for both the teams individually.
We all know that the formula of mean so sum of the items by number of items. We are going to use the same formula to get the answer.
So, the number of goals Spain scored per match is equal to the total number of goals divided by the total number of matches. We know that Spain scored $8$ goals in $7$ matches.
Therefore, number of goals Spain scored per match $ = \dfrac{8}{7}$
Similarly, the number of goals Brazil scored per match is equal to the total number of goals divided by the total number of matches. We know that Brazil scored $9$ goals in $5$ matches.
Therefore, number of goals Spain scored per match $ = \dfrac{9}{5}$
From the above result as \[\dfrac{9}{5} > \dfrac{8}{7}\], we can say that Brazil scored more goals than Spain per match.
When it comes to overall goals also, Brazil scored $9$ goals where Spain scored only $8$ goals.
Hence in the overall also Brazil scored more goals.

Note:Mostly when you are asked about the performance of the team which scored more goals per match, we use average value to determine them. It is also called as mean in terms of statistical data.In this kind of example means are rounded to the nearest integer as there will be no decimal number of goals. But be careful that decimal values also play a key role in other kinds of problems.