What is the formula for standard deviation?

The formula for standard deviation reflects how data points in a dataset deviate from the mean value, allowing for the assessment of variability within the data. The correct choice illustrates this key aspect by showing that standard deviation involves calculating the square root of the average of the squared differences from the mean.

To break it down, the process begins with determining the mean (or average) of the dataset. Then, for each individual data point, you find the deviation from the mean (which is the difference between the data point and the mean). These deviations are then squared to eliminate any negative values and to emphasize larger deviations. After obtaining these squared values, you compute their average by summing them up and dividing by the total number of observations, which gives you the variance.

Finally, taking the square root of this variance results in the standard deviation, which provides a measure that is in the same units as the original data, making it more interpretable. This methodology not only captures the dispersion of the dataset but also highlights the critical transformation of squaring deviations to handle their statistical significance appropriately.

While other options may incorporate elements of statistical calculations, only this choice accurately captures the steps involved in deriving the standard deviation, making it an essential and precise representation of how to quantify data