How do I work out the median?

By Henry Warren on the 11th of June, 2012

1 Answer

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    The Median is the middle number in a sorted list of numbers.For example to find the Median of 12,3 and 5. First put them in order ie 3,5,12.Then the middle number is 5 and so the median is 5

    Refine By jagadish on the 16th of January, 2013

Suggested reading…

Work out the median, quartiles and interquartile range

Mean = TOTAL of values/ NUMBER of values 

Median = MIDDLE value

Mode = MOST common value

Range = How far from the BIGGEST to the SMALLEST value

Let’s say you’re the teacher, and you want to get a feel for how well your class is learning. You assign them an assessment, and after marking the papers you create a list with all the students in order from the highest score, to the lowest score.

If you have 28 students in your class, then the score of the 14th student in your list (the one right in the middle) will be the median score for your class.

So the median is the score half way down the list, once you’ve arranged it in order. Now, let’s say the median score is 60% - how closely does that represent the average performance of the group? Did most people score around 60%, or actually did loads of people score 90%, and another bunch score around 25%? There’s a way of working this out.

If you look closer to the bottom of the list, towards the lower scores, and select the student who’s a quarter of the way up, their score would be the lower-quartile. In this case, the score of student number 7 would be the lower quartile for the class.

There’s an upper quartile as well. This is the score of the student who’s three quarters of the way up the list, near the top. For this class, the upper quartile is student number 21’s score.

The range for the class is the highest score minus the lowest score.

The inter-quartile range (IQR) for the class is the upper quartile minus the lower quartile.

The IQR tells you how accurate well the median value represents the who class performance. If the IQR is very small, that means most people scored around 60%. If the IQR is very large, however, then that means lots of people scored much higher, or lower, than 60%.

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