The median of a data set can be found depending on the number of data values in the set.
Median
For an odd number of data values arranged in numerical order, there is only one value in the middle, and that is the median.
For an even number of data values arranged in numerical order, the median is the average of the two middle numbers.
Since we are given a frequency table, we have to list each value from least to greatest and repeat according to its frequency.
80, 80, 80, 80, 80, 80, 85, 85, 85, 85, 90
90, 90, 90, 90, 90, 90, 90, 90, 90, 95
We listed a total of 21 data values, which is an odd number. Let's take a look at the student's work to see if we can find the mistake.
They took the average of two numbers! This is the mistake — they found the median as if they had an even number of data values! We will now find the median for an odd number of data values.
80, 80, 80, 80, 80, 80, 85, 85, 85, 85, 90
90, 90, 90, 90, 90, 90, 90, 90, 90, 95
The median of the given data set is 90.
