Reaching a New Average
Reaching a new average means finding the value needed on a future test or measurement to achieve a desired overall average. The method uses the formula: new value = (new average x total count) minus current total. For example, if your average on 3 tests is 80 and you want an 82 average after 4 tests, you need 4 x 82 - 3 x 80 = 328 - 240 = 88 on the fourth test. This skill is taught in Chapter 6 of Saxon Math Course 2 for 7th grade math and builds practical reasoning about averages that applies to academics and sports statistics.
Key Concepts
Property To find the value needed to achieve a new average, calculate the required total for the new average and subtract the current total. $$ \text{New Value} = (\text{New Average} \times \text{New Quantity}) (\text{Old Sum}) $$.
Examples Your average for 3 tests is 80. To get an average of 82 after 4 tests: New total needed: $4 \times 82 = 328$. Old total: $3 \times 80 = 240$. Score needed on the 4th test: $328 240 = 88$. After 4 bowling games, your average is 100. To get a 102 average after 5 games: New total: $5 \times 102 = 510$. Old total: $4 \times 100 = 400$. Score needed in game 5: $510 400 = 110$.
Explanation Time to level up your average! Figure out the total score you need for your new level (new average × new count). Then, subtract the score you already have (your current total) to see what you need on the next try to hit your goal.
Common Questions
How do you calculate what score you need to reach a new average?
Multiply your desired average by the total number of items, then subtract your current total. For example, to raise a 3-test average of 80 to an 82 average after 4 tests: 4 x 82 = 328, minus 3 x 80 = 240, so you need 328 - 240 = 88 on the next test.
What is the formula for reaching a new average?
The formula is: Needed Value = (Desired Average x New Count) - Current Sum. This works because the average equals the sum divided by the count, so you solve backwards from the target average to find the missing value.
Can you always reach any target average?
Not always. If the required score exceeds the maximum possible (like needing 110 on a 100-point test), the target average is unattainable. Calculating the needed score helps you determine whether a goal is realistic before the next test.
How is reaching a new average different from finding an average?
Finding an average means adding all values and dividing by the count. Reaching a new average works in reverse: you know the desired average and solve for the unknown value needed to achieve it. Both use the same sum-divided-by-count relationship.
When do students learn about reaching a new average?
This topic appears in 7th grade math, specifically in Chapter 6 of Saxon Math Course 2. It builds on students understanding of mean and extends it to practical problem-solving scenarios.
What is a real-world example of reaching a new average?
A basketball player averaging 15 points over 4 games wants to average 18 after 5 games. She needs 5 x 18 - 4 x 15 = 90 - 60 = 30 points in the fifth game. This type of calculation is common in sports, academics, and business.