What
are Standard Deviations?

Standard deviation is a commonly used
statistic, but it doesn’t often get the recognition it deserves. This form of
measurement is often used in casinos and Paddy Power Online Games,
explain: “Casino luck is quantified using standard deviations and games, such
as the slots, have extremely high standard deviations. This is demonstrated
when the size of the potential pay out increases and winnings move way over the
average result.”

Standard
deviation is a measurement of statistics that
specifically calculates how much your data spreads out. Showing the variation
in results, standard deviation highlights if the data collected scores close to
or far away from the average.

The more the data is spread out the greater the
standard deviation, but interestingly numbers cannot be negative with results
close to 0 indicating the data is close to the mean. This is useful in
comparing sets of data, which may have the
same mean but different statistics. Standard deviation gives you
extra insight into the overall data and there are two methods to calculate the
results.

Sample and Population Standard Deviations

When finding the standard deviation there are
two formulas available and depending on the type of data (either
sample or population) shows which you need to use. For example, if
the data was collected from one slot machine then you are looking at sample standard
deviation, but if you have data represents a range of machines then it would be
population standard deviation.

The formulas are broken down into sample and
population standard deviation to help achieve precise results for either type
of data. The steps in each formula are exactly the same accept for one and is
highlighted below:

Sample
Standard Deviation

Population Standard Deviation

Calculating Standard Deviation

Working out standard deviation by hand is rare
as it is a slow process and there are computer programs that do this for you.
Also the calculations involved are complex meaning it is easy to make a
mistake, however, by knowing the process it makes it easier to understand and
will show you how standard deviation really works.

By using the sample standard deviation formula
we can explain where the results come from and once broken down into easy steps
is simple to digest:

1.
Find the mean.

2.
For each data point, find the square of its
distance to the mean.

3.
Sum the values from Step 2.

4.
Divide by the number of data points.

5.
Take the square root.

The same can be said for population standard
deviation and like before if broken down into steps it is easy to follow:

1.
Calculate the mean of the data—this is μ
in the formula.

2.
Subtract the mean from each data point. These
differences are called deviations. Data points below the mean will have
negative deviations, and data points above the mean will have positive
deviations.

3.
Square each deviation to make it positive.

4.
Add the squared deviations together.

5.
Divide the sum by the number of data points in
the population. The result is called the variance.

6.
Take the square root of the variance to get the
standard deviation.

Checking Your Results

When looking at a typical standard
deviation on a graph it regularly represents a bell curve and can
help you predict your results. High in the middle and dropping to fewer
findings at either end the data collected often fits perfectly and makes sense
when you apply it to everyday scenarios.

For instance, buying a scratch card is similar
to playing on a slot
machine. When comparing winnings, the average person doesn’t win any
money and enjoys a burst of fun, whereas only a lucky few will win a large
amount of cash or unfortunately lose a lot.

Both these examples can be measured by standard
deviation and are likely to fit the typical bell curve graph. In most cases the
average will be around the same, even if the range of results vary greatly, and
only a few will receive big wins or losses.

Benefits of Standard Deviation

Standard deviation is a mathematical measurement
that is often overlooked, but once you become aware of what it does can have
many uses. It can also lead to finding other useful tools and can be applied to
a number of situations.

Another example is in a simple game like
roulette where the standard deviation can be beneficial, but understanding binomial
distribution is useful too. Binomial distribution is one of the simplest types
of distributions in statistics and provides either success or failure, such as
black or red and heads or tails.

By using binomial distribution and standard deviation together
it can help you understand how a game of roulette really works - even though it
can’t be applied in casinos. It can also be beneficial in many other scenarios, such as
making financial investments, so why not try it out
at home? This knowledge can be applied to a simple test, like
flipping a coin and once you know how it works, it could come in very useful.