What is the average (arithmetic mean) value of the integers from -50 to 50, inclusive?
a. -51/2
b. -25
c. 0
d. 25
e. 51/2
I'll be glad to check your answer.
is it C
Yes.
To find the average value of a set of integers, we sum up all the integers in the set and then divide by the total number of integers.
In this case, we want to find the average of the integers from -50 to 50, inclusive. To determine the total number of integers, we need to count how many integers are in this range.
The range from -50 to 50 covers 50 positive integers (including 0) and 50 negative integers (excluding 0). Therefore, the total number of integers is 50 + 50 + 1 = 101, where we add 1 for the number 0.
To find the sum of all the integers, we can use the arithmetic series formula: Sum = (first term + last term) * (number of terms) / 2.
The first term is -50, the last term is 50, and the number of terms is 101. Plugging these values into the formula, we get:
Sum = (-50 + 50) * (101) / 2
= 0 * 101 / 2
= 0
Thus, the sum of the integers from -50 to 50 is 0.
Finally, we divide the sum by the total number of integers to find the average:
Average = Sum / (number of integers)
= 0 / 101
= 0
Therefore, the average value of the integers from -50 to 50, inclusive, is 0.
So, the answer is c. 0.