Average
The average (arithmetic mean) is calculated by adding all values in a data set and dividing by the number of values. In Grade 6 Saxon Math Course 1, average = sum ÷ count. For test scores 85, 90, 78, 92, and 80: sum = 425, count = 5, average = 425 ÷ 5 = 85. The average represents the 'fair share' value — what each member would have if the total were redistributed equally. The average is also called the mean and is one of four statistical measures studied this year.
Key Concepts
Property To find the average of a set of numbers, we add the numbers to find the total and then divide the total by the number of numbers in the set to create equal groups. This is also called the mean.
Examples Find the average of 25, 30, and 35 students: $\frac{25 + 30 + 35}{3} = \frac{90}{3} = 30$ students. Find the average of the numbers 4, 9, and 11: $(4 + 9 + 11) \div 3 = 24 \div 3 = 8$. Find the average of 20, 30, 40, and 50 dollars: $\frac{20 + 30 + 40 + 50}{4} = \frac{140}{4} = 35$ dollars.
Explanation Think of 'average' as the 'fair share' number! Imagine you and your friends have different amounts of candy. To find the average, you first pool all the candy together into one giant pile (that's the 'adding' part). Then, you divide it all up evenly among everyone (that's the 'dividing' part). Now everyone has the same amount—the average!
Common Questions
What is the formula for average (mean)?
Average = Sum of all values ÷ Number of values.
Find the average of 85, 90, 78, 92, 80.
Sum = 425. Count = 5. Average = 425 ÷ 5 = 85.
What does the average represent?
The fair-share value: if the total were redistributed equally among all members, each would receive the average.
If the average of 4 numbers is 12 and three numbers are 9, 14, 11, what is the fourth?
Total = 4 × 12 = 48. Fourth number = 48 − (9 + 14 + 11) = 48 − 34 = 14.
Is the average always equal to one of the values in the data set?
Not necessarily. The average can be any value between the minimum and maximum, often not matching any specific data point.