Our sum of squares calculator is a very popular statistics calculator. To use this calculator, simply type in your list of inputs separated by commas (ie 2,5,8,10,12,18). Sum of squares is used in statistics to describe the amount of variation in a population or sample of observations. It is defined as being the sum, over all observations, of the differences of each observation from the overall mean.

A common use of statistics is to describe a population or sample of variables in mathematical terms. For example, a fast food franchise owner wants to examine the time it takes to serve drive through customers for his two stores. A simple analysis of the performance of the two stores for wait time can be described by the average, minimum, and maximum wait times. Although this information can be very useful it does not tell the whole story. Suppose the owner feels that not only should wait time be minimal, but that the wait times should be as consistent as possible. In order to evaluate their performance, the owner has the managers from stores A and B record the wait time for 50 random drive-through orders throughout the day. After the data was collected and analyzed the owner found store A to have the lower average wait time of 6.07 min to store B’s average of 6.98 min. But which store was more consistent?

The variation of wait time can be determined by the calculation for total sum of squares (SS). The larger the SS, the more variation is present for the population. SS = Σ(y − ȳ)2, where y is the observation and ȳ is the average. Although store A had lower wait times, store B was more consistent due to its lower SS of 0.92 versus store A’s 222.4.