A standard deviation is a statistic that measures the dispersion of a data set relative to its mean.

In addition, it is calculated as the square root of variance.

What is a standard deviation? …

A standard deviation is a statistical measurement. that highlights that individual data points of a data set are deviated from their mean.

In addition, if the data point is away from its mean, there is a high deviation or volatility.

and if the data point is near its mean, which means low volatility or low deviation from its mean.

Moreover, it is calculated as the square of the variance.

Key Takeaways…

• Standard deviation measures the dispersion of a data set relative to its mean.
• and it is calculated as the square root of the variance.
• In addition, finance is generally used to assess the relative riskiness of an asset.
• Moreover, a volatile stock has a high SD, and a blue-chip stock will have a low SD.

How standard deviation works?…

It is statistical measurement that is often used in finance, particularly in finance.

When it is applied to the annual return of an investment, it will provide information on that investment, i.e., historical volatility.

This means how much the price fluctuates over time.

In addition, the larger the standard deviation of the securities, the greater the variance between the variance between each price and mean.

Which shows a larger price range.

For example, volatile stock has a high SD, which means the price will move up and down frequently.

While at the same SD, a blue-chip stock will be low, which means its price will be stable.

 

Standard Deviation Forumulae…

SD is calculated by taking the square of the value derived from comparing data points to a collective mean of population.

 

Calculating Standard Deviation…

SD is calculated as follows…

• Calculate the mean of the data points.
• And the mean is calculated by adding all the data points and by dividing them by the number of data points.
• Now, the variance of each data point.
• In addition, the variance of each data point is calculated by substracting the mean from the value of the data point.
• Next, square the variance of each data point.
• Sum of squred squared variance values.
• Devide the sum of squared variance values by the number of data points in the data set.
• and take the square root of the quotient.

Standard deviation vs. variance…

Variance and SD are related to statistics.

In addition, variance is calculated by calculating the mean of the values and substracting the mean from each data point individually, squaring each of these results, and taking the other mean of the values.

When it comes to SD, it is the square root of the variance.

 

 

Examples of Standard Deviation…

If you have a data set with values 5, 7, 3, and 7.

First, add all the values. i.e., 5+7+3+7 = 22.

Find the mean of the data set by dividing the total by the number of data points in the data set.

i.e., 22/4 = 5.5.

This gives you xi = 5.5 and N = 4.

What does high standard deviation mean?…

A high SD means there is a lot of variance around the observed data mean.

In addition, this means that the data obtained is quite spread out.

and a low SD means the data being observed is clustered tightly near the mean.

What does the standard deviation tell you?…

SD describes how dispersed a set of data is.

And it compares each data point to the mean of all data points, and the standard deviation returns a calculated value that describes whether the data points are in close proximity or whether they are spread out.

Morover, In a normal distribution, the SD tells you how far values are from the mean.

Is a lower standard deviation better for investing?…

A lower SD isn’t necessarily better to invest in.

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