The goals scored by 40 football teams from three league divisions are recorded below No of goals 0 1 2 3 4 5 6…

Analysis

To find the total number of goals scored by all the teams, we need to calculate the sum of the products of each number of goals and its corresponding frequency. This is essentially finding the sum ($\sum fx$) from a frequency distribution table.

Concept

When given a frequency table, the total value of a data set is calculated by multiplying each value ($x$) by its frequency ($f$) and then adding all those products together. Formula: $\text{Total} = \sum (x \times f)$

Step-by-Step Solution

Let's multiply each number of goals by its frequency:

• 0 goals: $0 \times 4 = 0$
• 1 goal: $1 \times 3 = 3$
• 2 goals: $2 \times 15 = 30$
• 3 goals: $3 \times 16 = 48$
• 4 goals: $4 \times 1 = 4$
• 5 goals: $5 \times 0 = 0$
• 6 goals: $6 \times 1 = 6$

Now, add these products together to get the total number of goals: $\text{Total} = 0 + 3 + 30 + 48 + 4 + 0 + 6$

Calculation: $3 + 30 = 33$ $33 + 48 = 81$ $81 + 4 = 85$ $85 + 6 = 91$

The total number of goals scored by all the teams is 91.

Conclusion

Comparing our result to the given options: A. 21 B. 40 C. 91 D. 96

The correct option is C.

Exam Tip

In questions involving frequency tables, always double-check your multiplication before adding. A common mistake is to add the frequencies instead of the products, or to misread the table rows. Also, ensure the sum of your frequencies matches the total number of items mentioned in the question (in this case, $4 + 3 + 15 + 16 + 1 + 0 + 1 = 40$), which confirms you haven't missed any data points!