The standard deviation is a measure of the amount of variation or dispersion in a set of values. It is calculated as the square root of the variance. Given that the variance for the data set is 36 gallons, the standard deviation can be found by taking the square root of 36, which is 6. Therefore, the standard deviation for the number of gallons of oil produced each day is 6 gallons.
References:
* The concept of standard deviation and its calculation is a fundamental aspect of statistics, which is well- documented in statistical textbooks and resources.
* The calculation performed to arrive at the answer is based on the mathematical operation of taking the square root of the variance value.