average
(noun)
A measure of the "middle" or "typical" value of a data set.
Examples of average in the following topics:
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Averages
- In order to find the average, we must first find the sum of the numbers:
- Therefore, the average of the set of numbers $\{3,5,10\}$ is 5.
- Find the average of the following set of numbers: $\{12, 25, 34, 17, 8, 42\}$
- What is the average hourly wage of these 8 employees?
- Calculate the average of a set of numbers in a real-world context
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Difference Quotients
- The difference quotient is used in algebra to calculate the average slope between two points but has broader effects in calculus.
- The difference quotient is the average slope of a function between two points.
- To show how the above equation can be written as the average slope, put it into more familiar terms.
- The difference quotient can be used to calculate the average slope (here, represented by a straight line) between two points P and Q.
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The Distance Formula and Midpoints of Segments
- Another way to interpret this formula is an average: we average the $x$-coordinates to find the $x$-coordinate of the midpoint, and we average the $y$-coordinates to find the $y$-coordinate of the midpoint.
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Fitting a Curve
- the average of the $y$-coordinates {Let $\bar{x}$, pronounced $x$-bar, represent the mean (or average) $x$ value of all the data points.}
- the average of the $x$-coordinates {Respectively $\bar{y}$, pronounced $y$-bar, is the mean (or average) $y$ value of all the data points.}
- Now for the $y$-intercept, ($b$) one-eighth times the average of the $$$x$-coordinates: $\bar{x}=\frac{20}{8}=2.5$ and one-eighth times the average of the $y$-coordinates: $\bar{y}=\frac{13.5}{8}=1.6875$.
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Increasing, Decreasing, and Constant Functions
- The average rate of change of an increasing function is positive, and the average rate of change of a decreasing function is negative.
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Rates of Change
- How fast was his average speed over the course of the run?
- Using the graph, predictions can be made assuming that his average speed remains the same.
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Solving Problems with Inequalities
- Also, the average American consumes less than 10 grams of vitamin C every day.
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Summing Terms in an Arithmetic Sequence
- This can be thought of as $n$ times the average of the first and last terms.
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Addition and Subtraction; Scalar Multiplication
- Matrix addition, subtraction and scalar multiplication can be used to find such things as: the sales of last month and the sales of this month, the average sales for each flavor and packaging of soda in the $2$-month period.
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Problem-Solving
- According to the United States Census Bureau, over the last 100 years (1910 to 2010), the population of the United States of America is exponentially increasing at an average rate of one and a half percent a year (1.5%).