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Step 1: Subtract the mean from each of your numbers in your sample.
10 8 10 8 8 4
− 8 − 8 − 8 − 8 − 8 − 8
2 0 2 0 0 4
Step 2: Square all the differences.
10 8 10 8 8 4
− 8 − 8 − 8 − 8 − 8 − 8
2 2 0 2 2 2 0 2 0 2 4 2
4 0 4 0 0 16
Step 3: Add all the squared numbers together. This number is called the sum of squares.
10 8 10 8 8 4
− 8 − 8 − 8 − 8 − 8 − 8
2 2 0 2 2 2 0 2 0 2 4 2
4 + 0 + 4 + 0 + 0 + 16
= 24
Step 4: Divide the sum of squares by sample size -1 (n-1).
24 ÷ N – 1 = 24 ÷ 5
VARIANCE = 4.8
This value is the variance.
Standard Deviation
Standard deviation is a statistic that measures the degree of dispersion of a data set relative to its average. When
determining the deviation of each data point from the average, the standard deviation is calculated as the square root
of the variance. If the data points are farther from the mean, the greater the deviation in the data set; therefore, the
more spread out the data, the larger the standard deviation.
Using the previous example, we have to calculate the square root of the variance in order to find the standard derivation.
VARIANCE = 4.8
STANDARD DEVIATION = 4.8 = 2.19
Visual Representation of Data
In statistics or Artificial Intelligence, we deal with a huge volume of data. Whenever the amount of data increases rapidly,
an efficient and convenient data representation technology is needed. This complex and voluminous data, if expressed
visually, is better processed by the human brain. Hence, we require a graphical representation of data. Graphs not only
present data in a visual form but also reveal relations between variables and the trends in data sets.
Task Critical Thinking
Visit https://datavizcatalogue.com/ and study the different types of charts available.
The Data Visualisation Catalogue is a project developed by Severino Ribecca to create a (non-
code-based) library of different information visualisation types. The website serves as a learning
and inspiration resource for those working with data visualisation.
Maths for AI 183

