<< Chapter < Page | Chapter >> Page > |
Before you get started, take this readiness quiz.
One application of decimals that arises often is finding the average of a set of numbers. What do you think of when you hear the word average ? Is it your grade point average, the average rent for an apartment in your city, the batting average of a player on your favorite baseball team? The average is a typical value in a set of numerical data. Calculating an average sometimes involves working with decimal numbers. In this section, we will look at three different ways to calculate an average.
The mean is often called the arithmetic average. It is computed by dividing the sum of the values by the number of values. Students want to know the mean of their test scores. Climatologists report that the mean temperature has, or has not, changed. City planners are interested in the mean household size.
Suppose Ethan’s first three test scores were $85,88,\text{and}\phantom{\rule{0.2em}{0ex}}94.$ To find the mean score, he would add them and divide by $3.$
His mean test score is $89$ points.
The mean of a set of $n$ numbers is the arithmetic average of the numbers.
Find the mean of the numbers $8,12,15,9,\text{and}\phantom{\rule{0.2em}{0ex}}6.$
Write the formula for the mean: | $\text{mean}=\frac{\text{sum of all the numbers}}{n}$ |
Write the sum of the numbers in the numerator. | $\text{mean}=\frac{8+12+15+9+6}{n}$ |
Count how many numbers are in the set. There are 5 numbers in the set, so $n=5$ . | $\text{mean}=\frac{8+12+15+9+6}{5}$ |
Add the numbers in the numerator. | $\text{mean}=\frac{50}{5}$ |
Then divide. | $\text{mean}=10$ |
Check to see that the mean is 'typical': 10 is neither less than 6 nor greater than 15. | The mean is 10. |
The ages of the members of a family who got together for a birthday celebration were $16,26,53,56,65,70,93,\text{and}\phantom{\rule{0.2em}{0ex}}97$ years. Find the mean age.
Write the formula for the mean: | $\text{mean}=\frac{\text{sum of all the numbers}}{n}$ |
Write the sum of the numbers in the numerator. | $\text{mean}=\frac{16+26+53+56+65+70+93+97}{n}$ |
Count how many numbers are in the set. Call this $n$ and write it in the denominator. | $\text{mean}=\frac{16+26+53+56+65+70+93+97}{8}$ |
Simplify the fraction. | $\text{mean}=\frac{476}{8}$ |
$\text{mean}=59.5$ |
Is $59.5$ ‘typical’? Yes, it is neither less than $16$ nor greater than $97.$ The mean age is $59.5$ years.
Notification Switch
Would you like to follow the 'Prealgebra' conversation and receive update notifications?