**THIS IS AN IN CLASS EXCERCISE AND WILL NOT DIRECTLY AFFECT YOUR GRADE**

* Your solutions will be evaluated by the TAs to judge your knowledge of the material so please write neatly and keep your solution organized.

Problem #1: Recursively create the method public int power(int a, int b). The method will calculate a raised to the power b and return the result.

Problem #2: Recursively create the method public float round(float number, int precision). The method will round the number given to the precision specified. If the precision given is positive, round to the position numbered to the left of the decimal point. If the precision given is negative, round to the position numbered to the right of the decimal point. When rounding, round recursively each additional number to the right of your precision. Thus if the number 38237.87128746 was rounded to the precision -6, normally the four will be removed and the sixth column to the right of the decimal will remain as 7. In your solution, you would consider what is the right of precision -7, thus the 6 in precision -8 will round up. This will change precision -7 to 5, and then cause the final round to change precision -6 to 8, yielding 38237.871288 as the final result.

Problem #3: Recursively create the method public int mean(int list[]). The mean is defined as the average of all numbers in the list.

Problem #4: Recursively create the method public int mode(int list[]). The mode is defined as the number duplicated most in the list. You cannot assume the list is sorted. If you want it to be sorted, sort it. Consider this problem and create a solution for a sorted and an unsorted list.

Problem #5: Recursively create the method public int median(int list[]). The median is defined as the number at the midpoint of the list. If the list is even, the average of the two middle locations is taken.