# How do you find the mean and median of the data set: There are 28, 30, 29, 26, 31, and 30 students in a school's six Algebra l classes?

Dec 11, 2016

See explanation.

#### Explanation:

To find the mean of a data set you have to add all the values and divide the sum by the number of data:

$\overline{x} = \frac{28 + 30 + 29 + 26 + 31 + 30}{6} = \frac{174}{6} = 29$

To calculate the median you have to order the set first. The ordered set is:

$26 , 28 , 29 , 30 , 30 , 31$

Now you have to look for the middle term in the ordered set. If the number of all data is odd, then there is only one such number, else there are two such numbers. In the first case the number is the median, in the second case to calculate the median you have to find the mean of $2$ middle numbers.

This set has $6$ elements, so there are $2$ middle numbers:

$26 , 28 , \textcolor{red}{29} , \textcolor{red}{30} , 30 , 31$

$M e = \frac{29 + 30}{2} = \frac{59}{2} = 29.5$

Answer: The mean is $\overline{x} = 29$. The median is $M e = 29.5$.

Note: There is a way to check if you chose correct number(s) to calculate the median. There should be the same number of data on both sides of the middle number(s).