Finding the Total from an Average
Finding the total from an average uses the relationship Sum = Average x Quantity. If the average of five numbers is 20, their total sum is 5 x 20 = 100. This reverse calculation is useful when you know the mean but need the sum, such as finding total points scored across multiple games. The concept is covered in Chapter 6 of Saxon Math Course 2 and extends 7th grade students understanding of averages beyond just computing them from raw data.
Key Concepts
Property To find the sum of a group of numbers, multiply their average by the quantity of numbers in the group. $$ \text{Sum} = \text{Average} \times \text{Quantity} $$.
Examples The average of five numbers is 20. Their total sum is $5 \times 20 = 100$. Tisha averaged 15 points in 3 basketball games. She scored a total of $3 \times 15 = 45$ points.
Explanation Think of the average as the 'fair share' amount. If you know the fair share and how many people are sharing, you can find the total amount they have altogether by multiplying! It's like everyone temporarily had the exact same number.
Common Questions
How do you find the total from an average?
Multiply the average by the number of items. If the average score across 3 games is 15, the total is 3 x 15 = 45 points.
What is the formula for finding total from average?
Sum = Average x Quantity. This is the inverse of the average formula (Average = Sum / Quantity).
When would you need to find the total from an average?
When you know the average performance (like average points per game) and want to know the total across all events, or when solving word problems that give the mean instead of individual values.
Can you find a missing value if you know the average and other values?
Yes. Calculate the total using Sum = Average x Quantity, then subtract the known values. The remainder is the missing value.
What are common mistakes with this concept?
Students sometimes divide instead of multiply. Remember: to go from average to total, multiply by the count. To go from total to average, divide by the count.
Is this taught in 7th grade math?
Yes. Saxon Math Course 2 covers finding the total from an average in Chapter 6 as part of statistics and data analysis.