The variance measures how much the data are scattered about their mean. The variance is equal to the standard deviation squared.
Monitoring variance is essential to the manufacturing and quality industries because a reduction of process variance increases precision and reduces the number of defects. For example, a factory manufactures carpentry nails that are 50mm in length, and a nail meets specifications if its length is within 2mm of the target value of 50mm. The factory uses two types of machines to manufacture nails. Both machines manufacture nails with normally distributed lengths and a mean length of 50mm. However, nails from each machine have different variances: Machine A, with the solid-line distribution in the following figure, manufactures nails with a variance of 9mm2, and Machine B, with the dotted-line distribution in the following figure, manufactures nails with a variance of 1mm2. The distributions of nail length for each machine are superimposed, along with the vertical upper and lower specification bounds: