6.6 Median
The last type of average you will look at briefly is called the median. Put very simply, the median is the middle number in a set of data. The only thing you need to remember is to put the numbers in size order, smallest to largest, before you begin. As this is such a simple process let’s just look at two examples.
Case study _unit4.6.3 Example: Finding the median 1
Find the median of this data set:
Method
5, 10, 8, 12, 4, 7, 10
Firstly, order the numbers from smallest to largest:
4, 5, 7, 8, 10, 10, 12
Now, find the number that is in the middle:
4, 5, 7, 8, 10, 10, 12
8 is the number in the middle, so the median is 8.
Case study _unit4.6.4 Example: Finding the median 2
Find the median of this data set:
Method
24, 30, 28, 40, 35, 20, 49, 38
Again, you firstly need to order the numbers:
20, 24, 28, 30, 35, 38, 40, 49
And then find the one in the middle:
20, 24, 28, 30, 35, 38, 40, 49
In this example there are actually two numbers that are in the middle, you therefore find the middle of these two numbers by adding them together and then halving the answer:
(30 + 35) ÷ 2 = 32.5
The median for this set of data is 32.5.
If you want to see some more examples, or try some for yourself, use the link below:
https://www.mathsisfun.com/ median.html [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)]
Well done! You have now learned all you need to know about mean, median and range. The final part of this section, before the end-of-session quiz, looks at probability.
Summary
In this section you have learned:
that there are different types of averages that can be used when working with a set of data – range, mean, median and mode
range is the difference between the largest data value and the smallest data value and is useful for comparing how consistently someone or something performs
mean is what is commonly referred to when talking about the average of a data set
how to find the mean from both a single data set and also a set of grouped data
formulas and inverse operations to calculate missing data when given the mean of a data set
what the median of a data set is and how to find it for a given set of data.