First order the elements...
15, 27, 28, 34, 42, 52
The "five number summary" is minimum value, 1st quartile, median 3rd quartile and maximum value...
15, 27, 31, 42, 52
The "mean" is just the arithmetic (regular) average.
33
The sum of the squares of differences is just as it sounds for each number, subtract the mean and square it, and add all of those squares together...
760
Standard deviation is the square root of the variance which is the average of the sum of squared differences that we just calculated above...
It's about 11.25