Standard deviation is a fundamental statistical measure that tells us how spread out data points are from their average value. When data points cluster tightly around the mean, we have a small standard deviation. When they're scattered widely, we have a large standard deviation.
The first step in calculating standard deviation is to find the mean or average of your dataset. We add up all the data points and divide by the number of values. For our example with values 2, 4, 6, 8, and 10, the sum is 30, divided by 5 gives us a mean of 6.
Next, we calculate how far each data point is from the mean. This is called the deviation. For our example, we subtract 6 from each value: 2 minus 6 equals negative 4, 4 minus 6 equals negative 2, and so on. Then we square each deviation to eliminate negative values and emphasize larger differences.
Now we complete the calculation. First, we sum all the squared deviations: 16 plus 4 plus 0 plus 4 plus 16 equals 40. Next, we divide by the number of data points to get the variance: 40 divided by 5 equals 8. Finally, we take the square root of the variance to get our standard deviation: square root of 8 equals approximately 2.83.
To summarize: Standard deviation is a powerful tool that measures how spread out your data is. The process involves calculating the mean, finding deviations, squaring them, computing variance, and taking the square root. This gives you a single number that describes the variability in your dataset.