IBM Data Science Practice Test

What is the relationship between standard deviation and variance?

1. Standard deviation measures total data range

2. Variance simplifies the calculation of mean

3. Standard deviation is the square root of variance

4. Variance is always larger than standard deviation

The correct answer is: Standard deviation is the square root of variance

The relationship between standard deviation and variance is defined mathematically, with standard deviation being the square root of variance. Variance measures the average squared deviation of each data point from the mean, giving a sense of how spread out the data points are in relation to the mean. Since variance results in squared units (for example, if the data points are in meters, the variance will be in square meters), taking the square root of variance transforms it back into the original units of measurement. This transformation makes standard deviation a more interpretable measure of the spread of data, as it directly relates to the scale of the original data. This relationship is fundamental in statistics, as it allows analysts and researchers to discuss data variability in a more comprehensible form. Hence, understanding that standard deviation is derived from variance is critical in both theoretical and applied contexts in data analysis.