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Question Video: Solving Word Problems Involving the Mean of a Data Set Mathematics

In a soccer tournament, a team scored 32 goals with a mean of 2 goals per game. How many games did they play in total?

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Video Transcript

In a soccer tournament, a team scored 32 goals with a mean of two goals per game. How many games did they play in total?

We’ve been told the total number of goals scored by the team and the mean, or average, number of goals they scored per game. We can recall that the mean of a data set is calculated by dividing the sum of all the values in the data set by how many values there are. In this example, in which we’re interested in the mean number of goals scored per game, this corresponds to dividing the total number of goals scored by the team during the tournament by the number of games they played.

We’re given that the mean number of goals scored per game was two and that the total number of goals the team scored was 32. We don’t know the number of games played, and it’s this we need to calculate. Substituting the values we do know and using 𝑛 to represent the number of games played gives the equation two equals 32 over 𝑛. We can solve this equation in two ways.

The more formal approach is to first multiply both sides of the equation by 𝑛, leading to two 𝑛 equals 32. We can then divide both sides of the equation by two to give 𝑛 equals 16. The less formal approach would simply be to ask ourselves, 32 divided by what equals two? And of course, we should recall that 32 is twice 16, so 32 divided by 16 is two.

We’ve therefore found that the team played 16 games in total during the tournament.

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