The table shows the number of goals scored by a football team in each league match during a season.
\begin{tabular}{|c|c|}
\hline Number of goals scored & Frequency \\
\hline 0 & 2 \\
\hline 1 & 10 \\
\hline 2 & 7 \\
\hline 3 & 6 \\
\hline 4 & 3 \\
\hline 5 & 2 \\
\hline
\end{tabular}
a) Calculate the number of league games the team played over the season.
(1 mark)
b) Calculate the total number of goals scored by the team during the season.
(2 marks)
c) Calculate the mean average number of goals scored per match during the season.
Answer (2)
The football team played a total of 30 league games, scored 64 goals, and had a mean average of approximately 2.13 goals per match during the season.
;
Calculate the total number of league games: 2 + 10 + 7 + 6 + 3 + 2 = 30 .
Calculate the total number of goals scored: ( 0 × 2 ) + ( 1 × 10 ) + ( 2 × 7 ) + ( 3 × 6 ) + ( 4 × 3 ) + ( 5 × 2 ) = 64 .
Calculate the mean average number of goals scored per match: 30 64 = 2.1333... .
Round the mean to two decimal places: 2.13 .
Explanation
Understand the problem and provided data We are given a table that shows the number of goals scored by a football team in each league match during a season, along with the frequency of each score. We need to calculate the total number of league games played, the total number of goals scored, and the mean average number of goals scored per match.
Calculate the total number of league games a) To find the total number of league games, we sum the frequencies in the table. This is because each frequency represents the number of games with a particular number of goals scored.
Calculate the sum of frequencies The total number of league games is calculated as follows: 2 + 10 + 7 + 6 + 3 + 2 = 30 So, the team played 30 league games over the season.
Calculate the total number of goals scored b) To find the total number of goals scored, we multiply the number of goals scored in each match by the frequency (number of matches with that score) and then sum the results.
Calculate the weighted sum of goals The total number of goals scored is calculated as follows: ( 0 × 2 ) + ( 1 × 10 ) + ( 2 × 7 ) + ( 3 × 6 ) + ( 4 × 3 ) + ( 5 × 2 ) = 0 + 10 + 14 + 18 + 12 + 10 = 64 So, the team scored a total of 64 goals during the season.
Calculate the mean average number of goals scored per match c) To find the mean average number of goals scored per match, we divide the total number of goals scored by the total number of league games played.
Divide total goals by total games The mean average number of goals scored per match is calculated as follows: 30 64 = 2.1333... Rounding to two decimal places, the mean average number of goals scored per match is approximately 2.13.
State the final answer a) The number of league games the team played over the season is 30. b) The total number of goals scored by the team during the season is 64. c) The mean average number of goals scored per match during the season is approximately 2.13.
Examples
Understanding the average goals scored in football matches can help in predicting match outcomes and setting betting strategies. For instance, if a team consistently scores an average of 2 goals per match, analysts might use this information to estimate their scoring potential in future games. Similarly, coaches can use this data to assess their team's offensive performance and make strategic adjustments. This kind of analysis is also useful in fantasy football leagues, where predicting player performance is crucial for success. Knowing the average goals scored helps in making informed decisions about which players to include in your team.
