Tuesday, 10 January 2012

Mean, Mode, Median and Interquartile Range

I realise that stats test are not everyone ones favourite thing to do and that most people find them very confusing, with even the thought of a table of numbers quite scary......however, with practice they are not too bad and you could never be expected to do a entire stats test in an exam due to time constraints; so as long as you are prepared for them, they can be quite easy marks to get (hopefully!).

I am going to start with the basics and cover the measures of central tendency as well as Interquartile range which, as a measure of dispersion, would perhaps be better placed with Standard Deviation. Any AS students reading this, apologises for the frequent references to Poole but I hope it still helps! The other 4 stats tests are quite lengthy so I will do a separate post for each one - they will hopefully appear very soon!

MEAN:- Add the numbers up and divide by the numbe of numbers
---> Often favoured over mode and median as takes into account extreme values, which the others disregard.
e.g 2,4,6,8,10,12,14
Mean = 56
          = 8
MODE:- Most common number - if no number is more common then there is 'no mode'
e.g 2,4,6,8,10,12,14
Mode= no mode
e.g 2,2,4,6,6,6,8,10,10,12,14
Mode = 6
---> In Poole fieldwork it could be used to calculate which is the most common bird found in Holes Bay, for example
MEDIAN:- the (n+1) = value
e.g 2,4,6,8,10,12,14
Median = 4th value = 8
---> Could be used after traffic counts to estimate daily/weekly traffic flows across a particular area

---> If a set of values has a symmetrical distribution (normal distribution), the mean, mode and median will be at the same place. However, if the distribution is skewed, the mode will still be at the point of highest frequency but the median and mean will each lie elsewhere.

INTERQUARTILE RANGE (IQR) :- Distance between the 75th percentile (UQ) and the 25th percentile (LQ)
---> IQR is a measure of dispersion, with the bigger the IQR, the wider the distribution in the data.
---> Often used to draw 'box and whisker plots'/dispersion diagrams as they illustrate spread of a number of values around the mean value, enabling a comparison of spread and/or bunching of data.
---> IQR and Standard Deviation both measure dispersion (spread), but IQR is more resistant to outliers whilst Standard Deviation is sensitive to outliers and extreme observations.
Lower Quartile (LQ) = (n+1) = value
Upper Quartile (UQ) = 3(n+1) = value
e.g 2,4,6,8,10,12,14
LQ = (7+1) = 2nd value = 4
UQ = 3(7+1) = 6th value = 12
IQR = 12 - 4 = 8

Hopefully most people are okay with this, just ask though if you would like a worked example from the AIB.....
Standard Deviation and Spearman's Rank are on the way (I will probably do Chi Squared and Mann Whitney U at some point later this week - AS students, you are lucky enough not to have to know these two yet!).

As always, let me know if I have made any mistakes or if there is anything else you would like me to cover!!!


  1. What does n represent in your equations???? Thank you in advance!!!

    1. n represents the number of samples/data points etc so in all the examples above n=7

  2. What does n represent in your equations???? Thank you in advance!!!