Standard Deviation Formula

Most of the statisticians prefer not to calculate the standard deviation by hand because it involves risk of making mistakes and also the calculations are complex in nature. The manual calculation is also very slow i.e. why statisticians rely on spreadsheets and computer software to calculate their numbers.

Now you must be wondering that why we are investing so much of time to learn about the above mentioned topic which in general the statisticians don't actually use. The answer is that by doing so will give us insight into how standard deviation really works.

Definition

Standard deviation is a number that measures the propagation of a data group corresponding to its accuracy. The standard deviation is calculated as the square root of the variation by determining the deviation of each data point as compared to the truth. If the data points move away from the set, then there is more difference within the data set. Thus, the larger the data spread, the greater the standard deviation.

Points to be noted

The standard deviation measures the spread relative to the spread of a data group.

A volatile stock will have a high standard deviation while a stable volatile stock will usually have a low standard deviation.

As a disadvantage, standard deviation treats any type of uncertainty as a risk even if it is in the investor's favor - such as income above average.

Understanding Standard Deviation

Standard deviation which is also known as SD in short form is a statistical measure in finance that when applied to an investment's annual rate of return, highlights the historical volatility of that investment. The higher the standard deviation of the securities is the greater the variance will be between each price and the average, which represents a larger price range. For example, a volatile stock has a high standard deviation while a stable blue chip stock has a low deviation.

Calculating Standard Deviation

The standard deviation is calculated as follows:

1. Average value is calculated by adding all the data points and dividing by the number of data points.

2. The variance for each data point is calculated by subtracting the average from the value of the data point. Then each of those resulting values is squared and the result is summed. Then one less, the result is divided by the number of data points.

3. Then the result of the number 2—the square root of the variance—is used to derive the standard deviation.

Standard deviation formula

Steps to find

Step 1: Find the mean.

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

Step 3: Sum the values from Step 2.

Step 4: Divide by the number of data points.

Step 5: Take the square root.

Also read:Break Even Point Analysis

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