​What's the difference between the mean, median and mode? Why are there so many different types of average?!

The average we're all familiar with is called the mean average - "add them all together and divide by how many there are", but sometimes another type of average makes more sense.

As an example, consider a company with 8 employees, earning the following amounts per week.


For the mean average, we add them all together (to give £8000), then divide by how many there are (8 of them), to give £1000 a week - this is the mean average weekly wage of the company, but all but one of the employees earns less than this, the average is skewed (messed up) by the boss who gets way more money than everyone else!

For the median average, we list the amounts in ascending or descending order (conveniently, this has already been done), then select the middle salary. Since there are an even number of employees, there are two values which are both equally in the middle - £280 and £300 - so we take a (mean!) average of those two. The median average is £290 a week.

In this case, the median average (£290/week) gives a better idea of the wages of a typical employee, compared with the mean average (£1000/week).

The mode average is usually used when data are in categories, such as shoe sizes, and is simply the category which occurs most often.

For example, here is a table of shoe sizes and frequencies for a class of 27 year 11 pupils.

Size    |    frequency
 6        |    2
 7        |    3
 8        |    4
 9        |    8
10       |    5
11       |    4
12       |    1

the mode is simply the category which occurs most often, in this case the shoe size 9, with 8 people in the class having that shoe size.

John H. GCSE Maths tutor, A Level Maths tutor, A Level Further Mathem...

9 months ago

Answered by John, a GCSE Maths tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist


£18 /hr

Henry P.

Degree: MChem Chemistry with a Year in Industry (Masters) - Cardiff University

Subjects offered: Maths, Physics+ 2 more

-Personal Statements-

“About Me: I am studying Chemistry at Cardiff University and am now in my second year having passed with a first in all my modules last year. I really love all things science and have a real drive to pass on what I know to other people....”

£18 /hr

Izzy S.

Degree: English Literature (Bachelors) - Durham University

Subjects offered: Maths, History+ 1 more

English Literature

“Hi! I’m Izzy and I’m a first year English Literature Student at Durham University. I studied English Literature, History, and Maths at A Level so I’m experienced in learning and teaching a variety of different subjects and ways of thi...”

£18 /hr

Michael L.

Degree: Medicinal Chemistry (Masters) - Leeds University

Subjects offered: Maths, Science+ 1 more


“I am currently in the penultimate year of my Masters degree in Medicinal Chemistry at the University of Leeds. At present, I'm averaging first class marks. Alongside my studies, I am a keen cyclist and am a cycling leader with Leeds R...”

MyTutor guarantee

About the author

John H.

Currently unavailable: until 20/11/2016

Degree: PhD in Metallurgy and Materials ("solubility and particulate release behaviour of corrosion films on SS316L surfaces in simulated PWR primary coolant") (Doctorate) - Birmingham University

Subjects offered: Maths, Physics+ 1 more

Further Mathematics

“About me:Hi there. I'm in the final year of a PhD at the University of Birmingham, writing up my thesis. I'm still learning!I love maths and physics - there's so much cool stuff, especially at A Level. I still remember when I first ...”

You may also like...

Other GCSE Maths questions

What if my equation doesn't factorise?

Solve 5x^2 - 9x + 4 = 0 using the quadratic formula

The area of a square is 49cm^2. The perimeter of the square is equal to the circumference of a circle. what is the radius of the circle?

There are 20 coloured balls in a bag. The probability of choosing a red ball at random is 1/4. One more red ball is added. Work out the probability of choosing a red ball.

View GCSE Maths tutors


We use cookies to improve our service. By continuing to use this website, we'll assume that you're OK with this. Dismiss