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:  

https://statistics.laerd.com/statistical-guides/img/standard-deviation-1.png  

  Sample Standard Deviation

 

https://statistics.laerd.com/statistical-guides/img/standard-deviation-2.png

  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 https://upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Standard_deviation_diagram.svg/400px-Standard_deviation_diagram.svg.pngit 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.