Which of the following represents the calculation of variance?

The calculation of variance is represented correctly in the choice provided. Variance measures how spread out the values in a data set are from the mean. It is computed by taking the difference between each data point and the mean, squaring that difference to ensure all values are positive, and then averaging those squared differences.

The correct formula starts with the values of the data set. For each value, you subtract the mean and square the result to eliminate any negative values and give greater weight to larger deviations. Summing those squared values reflects the total spread away from the mean, and dividing by the number of values (or, in some cases, the number of values minus one for a sample) gives a measure of the average spread, which is the variance.

This method is fundamental in statistics as it provides insights into how much variability exists in the data set, which is crucial for further statistical analysis and interpretations. Understanding variance is key for studies involving data distribution and standard deviation, as standard deviation is simply the square root of the variance.