**Mean**

There are four types of average: mean, mode, median and range. The mean is what
most people mean when they say 'average'. It is found by adding up all of the
numbers you have to find the mean of, and dividing by the number of numbers. So
the mean of 3, 5, 7, 3 and 5 is 23/5 = 4.6 .

When you are given data which has been grouped, the mean is Sfx
/ Sf , where f is the frequency and x is
the midpoint of the group (S means 'the
sum of').

*Example*: Work out an estimate for the mean height.

Height (cm) Number of People (f) Midpoint (x)
fx (f multiplied by x)

101-120
1
110.5
110.5

121-130
3
125.5
376.5

131-140
5
135.5
677.5

141-150
7
145.5
1018.5

151-160
4
155.5
622

161-170
2
165.5
331

171-190
1
180.5
180.5

Sfx = 3316.5

Sf = 23

mean = 3316.5/23 = __144cm__ (3s.f.)

**Mode**

The mode is the number in a set of numbers which occurs the most. So the modal
value of 5, 6, 3, 4, 5, 2, 5 and 3 is 5, because there are more 5s than any
other number.

**Range**

The range is the largest number in a set minus the smallest number. So the range
of 5, 7, 9 and 14 is (14 - 5) = 9.

**The Median Value**

The median of a group of numbers is the number in the middle, when the numbers
are in order of magnitude. For example, if the set of numbers is 4, 1, 6, 2, 6,
7, 8, the median is 6:

1, 2, 4, **6**, 6, 7, 8 (6 is the middle value when
the numbers are in order)

If you have n numbers in a group, the median is the (n + 1)/2 th value. For
example, there are 7 numbers in the example above, so replace n by 7 and the
median is the (7 + 1)/2 th value = 4th value. The 4th value is 6.

© Matthew Pinkney