Succeed with maths: part 2
Succeed with maths: part 2

Start this free course now. Just create an account and sign in. Enrol and complete the course for a free statement of participation or digital badge if available.

1.3 Calculating the median value of a data set

The median is defined as the middle value of a data set when all the data is arranged in numerical order. If there is an even number of values, and therefore no middle value, then the median is calculated as the mean value of the two middle values.

So, let’s now see how using the median, rather than the mean, affects the value for the average rainfall in Vermont. Here’s a reminder of the data:

Table _unit8.2.3 Table 3 Precipitation (rainfall) in Vermont for October 2007–2011
Year 2007 2008 2009 2010 2011
Rainfall, in inches (to 1 d.p.) 5.8 5.2 4.6 9.3 4.5
(Enloe, 2013)

To find the median rainfall, first arrange the data values in numerical order, to give:

4.5 4.6 5.2 5.8 9.3

There are five data values, an odd number, so the median is the middle value in this case. Therefore the median rainfall is 5.2 inches.

If you look at the number line again in Figure 2, with the median added this time, it appears that the median may be a better choice for an average or typical value in this case:

Figure _unit8.2.2 Figure 2 Rainfall number line with mean and median values indicated

Now try out the next activity.

Activity _unit8.2.3 Activity 3 A computer game for Charlie

Timing: Allow approximately 7 minutes

Over the course of one week Charlie plays her computer game every day except Friday, and achieves the following scores:

Table _unit8.2.4 Table 4 Charlie's computer game scores over one week
Monday Tuesday Wednesday Thursday Saturday Sunday
250 270 300 290 290 270
  • a.Find Charlie’s mean score over these seven days.


  • a.To find the mean, find the sum of the scores and divide by the number of scores, six.

    Charlie’s mean score = 250 + 270 + 300 + 290 + 290 + 270 = 278 (to the nearest whole number).

  • b.Find Charlie’s median score over these six days. (Click on reveal comment if you would like a hint)


There is an even number of data values this time, so to find the median calculate the mean of the middle two values.


  • b.To find the median score, arrange the data values in order:

    250 270 270290 290 300

    There is an even number of values (six), so Charlie’s median score is the mean of the two middle values, 270 and 290.

    Median score equation sequence equals 270 plus 290 divided by two equals 280
  • c.How do the median score and the mean score compare in this case?


  • c.This time, the mean and median scores are very close. This is because the data values are fairly evenly clustered around the mean value without any extremely high or low values.

Having covered the mean and median, this leaves just the mode to consider in the next section.

Take your learning further

Making the decision to study can be a big step, which is why you'll want a trusted University. The Open University has 50 years’ experience delivering flexible learning and 170,000 students are studying with us right now. Take a look at all Open University courses.

If you are new to University-level study, we offer two introductory routes to our qualifications. You could either choose to start with an Access module, or a module which allows you to count your previous learning towards an Open University qualification. Read our guide on Where to take your learning next for more information.

Not ready for formal University study? Then browse over 1000 free courses on OpenLearn and sign up to our newsletter to hear about new free courses as they are released.

Every year, thousands of students decide to study with The Open University. With over 120 qualifications, we’ve got the right course for you.

Request an Open University prospectus371