# Standard Deviation

## Understanding and Calculating Standard Deviation

If you are studying statistics, it is essential to have a grasp on measures of central tendency before delving into standard deviation. For those familiar with mean, let's continue!

### Defining Standard Deviation

Standard deviation is a measure of how much the values in a data set vary from the mean. It is useful in determining the spread of data points from the average.

### The Formula for Standard Deviation

The standard deviation formula is:

σ = √(∑(x-μ)^2/N)

Where:

• σ represents standard deviation
• stands for sum
• x is an individual number in the data set
• μ is the mean of the data set
• N is the total number of values in the data set

In simpler terms, standard deviation is calculated by finding the square root of the sum of the squared difference between each data point and the mean, divided by the total number of data points.

### Why Standard Deviation is Significant

Standard deviation is a valuable tool for predicting the probability of data points falling within a certain distance from the mean. It assumes that the data points follow a normal distribution, with values evenly spread around the mean in a bell-shaped curve.

The visual representation of a normal distribution can be seen in the graph below:

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