Final answer:
The arithmetical average refers to the mean, which is the sum of all values in a data set divided by the number of values. It is a measure of central tendency, different from the median or mode, and is used to represent the typical value in a data set.
Step-by-step explanation:
The "arithmetical average" is another term for the mean. The mean represents the central tendency of a data set and is calculated by adding all values in the sample and dividing by the number of values. This is distinct from the median, which is the middle value in an ordered data set, and the mode, which is the most frequently occurring value. Regarding a symmetrical distribution of data, the mean, median, and mode will be the same, located at the central high point of the distribution. However, in skewed distributions, the mean is typically pulled towards the tail, reflecting the skewing the most.
For the data set provided (10; 11; 15; 15; 17; 22), the mean can be calculated by adding these numbers and dividing by the count of numbers, which in this case is 6. If required, a standard deviation can be calculated to understand the spread of data around the mean. Identifying a number that is two standard deviations above the mean would involve calculating the standard deviation and then adding twice this value to the mean.