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What the formula essentially says is that you take each element (number) in the
dataset, you add them all together to get the total sum, and then you divide the
sum achieved by the total number of elements (numbers) in the dataset. Taking
an example to understand this concept:
1. Dataset = {1,2,3,4}
To calculate its mean, we first need the sum of the elements which is 1+2+3+4 =
10 and then total number of elements is 4 so the mean is:
M(X) = 104= 2.5 (2)
2.1.2 Median
In simple terms, the median gives us the middle value of the dataset: in other
words the midpoint around which the points in the dataset are scattered around.
There are a few rules to calculating the median which can be expressed as
follows and must be read with great care:
1. Irrespective of how many number there are in the dataset, the first step is
always to arrange the numbers in ascending order (starting from the smallest
number and ending with the largest number)
2. Start crossing out one element from the left side and simultaneously, one from
the right hand side until you arrive at the middle. If only one value is left at the
end, then that’s the answer. If there are two values at the end, you take their
average x
1+x2
2 where x1 and x2 are the two numbers.
There’s also another method to calculate the median using a formula. Both would
be marked correct in the IGCSE papers. For this method you have to first
determine whether there are odd number of elements or even number of
elements. Once done, move on the final step for each one as follows:
2
1. If there are an even number of elements, the formula is ( N2)+( N+1 2)
N is the total number of elements
2 where
2. If there are an odd number of elements, the formula is again the same with the
N the number of elements: N+1
2
2.1.3 Mode
Mode refers to the value that’s repeated the most in the dataset. So let’s say we
have the dataset:
D = {1, 2, 3, 4, 4, 4} (3)
4 is repeated the most (a total of 3 times) while all other numbers are just written
only once. Therefore, your mode would be 4.
2.1.4 Range
Range refers to the spread of the data, how far away from the midpoint your data
is, without considering the variance of the dataset. There’s only one formula in the
IGCSE syllabus to calculate it:
R = Ymax − Ymin (4)
Here Ymax is the largest number in the dataset and Ymin is the smallest number in
the dataset. So if we have the same dataset the range would be:
R = 4 − 1 = 3 (5)
2.2 Grouped Data - Calculating Mean and Mode
Grouped data is a form of data representation in table-form where instead of
separate independent categories, there are certain intervals given for each row.
An example can be seen below which will be used for all calculations of this
section: The interval for ages is what makes this a grouped data. All the