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154
Statistics
1 Classifying Statistical Data
1.1 Classify and tabulate statistical data
This section deals with how to read and interpret tables properly, classifying the dataset as we go forwards.
We need to know two main types of tables for this part of the syllabus:
1. Tally Tables
2. Two-way tables
Item
Frequenc
y
Tally
Group A
Group B
Total
Apples
Oranges
Bananas
Grapes
5
3
6
4
|||||
| | |
| | | | | |
| | | |
Categ
ory 1
Categ
ory 2
Categ
ory 3
12
10
7
8
15
13
20
25
20
Total
29
36
65
The table on the left hand side is called a tally table. The first column tells us what item/object we are
talking about. Frequency in the second column refers to the number of occurrences of that item/object. For
example a frequency of 5 for the apples means there are 5 apples. The last column is what we call the tally
column. Each vertical line is equivalent to 1 tally and we represent the number using these vertical lines.
However, as you may have already noticed, this is a very inefficient way of representing data especially if
the frequency of the independent variable is very large, for example 100 or 1000.
The table on the right hand side represents a two-way table. Any table would have some kind of categories.
It’s called a two-way table as it has categories in both the rows and columns. For example in the columns
we have groups like A and B and total, and in the rows we have the categories of an object and then the
total row. This makes writing data more efficient. A way to interpret such tables is to always keep in mind
the row and column you are reading. For example, I ask myself a question:
1. What does the 13 in the table represent?
The answer to that: It lies in the group B column so must be related to Group B and it lies in the Category
13 row so must be related to that so it means either of the following things since they are both the same:
1
1. The number of category 3 objects that are group B too
2. The number of group B objects that are category 3 objects too
2 Interpreting Statistical Data
2.1 Statistical Methods of Evaluation to compare two or more datasets
2.1.1 Mean/Average
The mean is a mathematical evaluation of the central tendency of the dataset provided. Mathematically in
the IGCSE syllabus, it can be defined as the following where X represents a dataset:
PN
i=1 xi
M(X) =
N=x1 + x2 + x3 + . . . xN
N(1)