Final answer:
Statistics such as mean, median, mode, and standard deviation are measures to describe data sets. In a symmetrical distribution, these measures are equal. Calculations for mean and standard deviation are based on data values and their distribution.
Step-by-step explanation:
The statistics in question include mean, median, mode, and standard deviation. These are all measures used to describe data sets. The mean is the average of all the numbers in the data set. The median is the middle value when the data is ordered. The mode is the most frequently occurring value in the set. Standard deviation measures how spread out the numbers are from the mean.
In a symmetrical distribution, the mean, median, and mode are all equal. This equality occurs because the data is evenly distributed around the center point.
To compute the mean of the given data set (10, 11, 15, 15, 17, 22), you add all the numbers together and divide by the number of values. For the standard deviation, you would calculate the variance by taking each number's deviation from the mean, squaring it, summing these squares, dividing by the number of values minus one for a sample, and then taking the square root of that result. If a number is two standard deviations above the mean, it is the mean plus two times the standard deviation.