Data Analytics: Practical Guide to Leveraging the Power of Algorithms, Data Science, Data Mining, Statistics, Big Data, and Predictive Analysis to Improve Business, Work, and Life

Measures of dispersion include the range, the variance, and the standard
deviation. They help us see how the scores are spread out, and if they are
close together or widely spread apart.
The range is the spread of figures from the lowest one to the highest. In
other words, it describes the distance from the lowest to the highest score.
The variance measures how far our set of random numbers are spread out
from the mean. Are they clustered together around this point, or are there
wide variations in value? It’s calculated by first subtracting the mean from

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each of the numbers in our set. (This shows the distance of that figure from
the mean.) Each of these answers are then squared, the sum of the squares
found, then divided by how many numbers there are in the set.
The standard deviation refers to the average shift of scores from the mean.
To find it, we’d measure how far all our figures are from the mean, then
square each of them. We’d then find the sum, thus getting a result known as
the variance. When we then calculate the square root of the variance, we
will have the standard deviation.
 

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Inferential Statistics
 
When research is done on groups of people, usually both descriptive and
inferential statistics are used to analyze results and arrive at conclusions.
Inferential statistics are useful when we just want to use a small sample
group to infer things about a larger population. So, we are trying to come to
conclusions that reach past the immediate data that we actually have on
hand.
They can help to assess the impact that various inputs may have on our
objectives. For instance, if we introduce a bonus system for our workers,
what might the productivity outcome be?
Inferential statistics can only be used if we have a complete list of the
population members from which we have taken our sample. Also, the
sample needs to be big enough.
There are different types of inferential statistics, some of which are fairly
easy to interpret. An example is the confidence level. If say, our confidence
interval is 98%, it means that we are 98% confident that we can infer the
score of a population based on the score of our sample.
Inferential statistics therefore allow us to apply the conclusions from small
experimental studies to larger populations that have actually never been
tested experimentally. This means then, that inferential statistics can only
speak in terms of probability, but it is very reliable probability, and an
estimate with a certain measurable confidence level.
 

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