# How do you find the median of the data set 88.6, 87.8, 85.3, 89.3, 86.8, 88.3, 85.9, 89.0, 87.4?

Oct 2, 2017

$87.8$

#### Explanation:

The median of a set of data values is the middle value, after sorting the values from low to high.
So to start we need to put the data in order.

$85.3 , 85.9 , 86.8 , 87.4 , 87.8 , 88.3 , 88.6 , 89.0 , 89.3$

If we cross off a value from each end, we will finish with the middle data value.

$\cancel{85.3} , 85.9 , 86.8 , 87.4 , 87.8 , 88.3 , 88.6 , 89.0 , \cancel{89.3}$

$\cancel{85.3} , \cancel{85.9} , 86.8 , 87.4 , 87.8 , 88.3 , 88.6 , \cancel{89.0} , \cancel{89.3}$

$\cancel{85.3} , \cancel{85.9} , \cancel{86.8} , 87.4 , 87.8 , 88.3 , \cancel{88.6} , \cancel{89.0} , \cancel{89.3}$

$\cancel{85.3} , \cancel{85.9} , \cancel{86.8} , \cancel{87.4} , 87.8 , \cancel{88.3} , \cancel{88.6} , \cancel{89.0} , \cancel{89.3}$

And we are left with the middle data value of $87.8$ which is our median.

Extra: When the data contains an even number of values, crossing one off from each end will eventually leave you with two values in the middle, instead of one. In this case, the median is defined to be the mean (or average) of these two middle values.

Example: For the set $\left\{1 , 1 , 2 , 3 , 5 , 8\right\} ,$ the middle two values are 2 and 3, and so the median of this set is halfway between 2 and 3, which is $\frac{2 + 3}{2} = \frac{5}{2} = 2.5 .$