Create an array of numbers filled by the random number generator. Determine the smallest, largest, average, and calculate the standard deviation. Allow the client to pick the size of the array to be used and allow the client to repeat the process with a new array. In statistics and probability theory, the standard deviation shows how much variation or dispersion from the average exists in a group of numbers. A low standard deviation indicates that the data points tend to be very close to the mean (also called expected value); a high standard deviation indicates that the data points are spread out over a large range of values. For a finite set of numbers, the standard deviation is found by taking the square root of the average of the squared differences of the values from their average value. For example, consider a population consisting of the following eight values: 2, 4, 4, 4, 5, 5, 7, 9. These 8 data points have the mean (average) of 5. (2 + 4 + 4 + 4 + 5 + 5 + 7 + 9)/8 = 5. Calculate the difference of each data point from the mean (average) and square this value.
(2 - 5)2 = (-3)2 = 9 (5 - 5)2 = (0)2 = 0
(4 - 5)2 = (-1)2 = 1 (5 - 5)2 = (0)2 = 0
(4 - 5)2 = (-1)2 = 1 (7 - 5)2 = (2)2 = 4
(4 - 5)2 = (-1)2 = 1 (9 - 5)2 = (4)2 = 16
Next, calculate the mean of these values: (9 + 1 + 1 + 1 + 0 + 0 + 4 + 16)/8 = 4. Now take the square root of the mean. The square root of 4 is 2 which is the standard deviation.