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The ages of the four students in Ben’s carpool are Find the mean age of the students.
21.5 years years
Yen counted the number of emails she received last week. The numbers were Find the mean number of emails.
10
Did you notice that in the last example, while all the numbers were whole numbers, the mean was a number with one decimal place? It is customary to report the mean to one more decimal place than the original numbers. In the next example, all the numbers represent money, and it will make sense to report the mean in dollars and cents.
For the past four months, Daisy’s cell phone bills were Find the mean cost of Daisy’s cell phone bills.
| Write the formula for the mean. | |
| Count how many numbers are in the set. Call this and write it in the denominator. | |
| Write the sum of all the numbers in the numerator. | |
| Simplify the fraction. | |
Does seem ‘typical’ of this set of numbers? Yes, it is neither less than nor greater than
The mean cost of her cell phone bill was
Last week Ray recorded how much he spent for lunch each workday. He spent Find the mean of how much he spent each day.
$7.19
Lisa has kept the receipts from the past four trips to the gas station. The receipts show the following amounts: Find the mean.
$39.62
When Ann, Bianca, Dora, Eve, and Francine sing together on stage, they line up in order of their heights. Their heights, in inches, are shown in [link] .
| Ann | Bianca | Dora | Eve | Francine |
|---|---|---|---|---|
Dora is in the middle of the group. Her height, is the median of the girls’ heights. Half of the heights are less than or equal to Dora’s height, and half are greater than or equal. The median is the middle value.
The median of a set of data values is the middle value.
What if Carmen, the pianist, joins the singing group on stage? Carmen is inches tall, so she fits in the height order between Bianca and Dora. Now the data set looks like this:
There is no single middle value. The heights of the six girls can be divided into two equal parts.
Statisticians have agreed that in cases like this the median is the mean of the two values closest to the middle. So the median is the mean of The median height is inches.
Notice that when the number of girls was the median was the third height, but when the number of girls was the median was the mean of the third and fourth heights. In general, when the number of values is odd, the median will be the one value in the middle, but when the number is even, the median is the mean of the two middle values.
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