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The Key Mathematical Ideas Behind Standardised Tests

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The key mathematical ideas behind standardised tests
All standardised test scores are based on the theory that a candidate’s score can be compared with the scores of others who have previously completed a test (based on a standardised sample). The scores of the candidates who previously undertook the test can be plotted in a graph that will resemble a “normal” curve. (DISCUSS PECENTILES AND STANDARDS SCORES ETC).
The various forms of averages and how they are calculated
Mean
The mean is calculated by adding up all the numbers in a dataset and then dividing that by the number of values in that dataset. An example is given below of a dataset of six students and their test scores out of 20:
S1 S2 S3 S4 S5 S6 Total Divided by: Mean
18 16 17 13 14 19 97 6 16.17

In order to find the mean test score, the total amount scored (97) is divided by the number of students (6) which equals 16.17.
The formula for calculation the mean is as follows: _
X
is the symbol for the mean and is referred to as bar X (ex) Σ is the Greek symbol sigma and simply means sum or add up X refers to each of the individual values that make up the dataset n is the number of values that make up the dataset
The use of mean is effective when the values of the dataset are evenly spread with no extreme high or low values. If the dataset does contains one or two extremely high or low values the result will be adversely affected by this.
An example of this is given below, where S1 and S4 are much lower than the other variables.
S1 S2 S3 S4 S5 S6 Total Divided by: Mean
2 16 17 3 14 19 71 6 11.83

If a dataset does containing extremely low or extremely high values, then the median is a better way of measuring average value.
Median
This refers to the middle value in a dataset, where values are arranged from lowest to highest and vice versa. When the dataset has

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