206k views
0 votes
What is the absolute difference between the mean and median of the first 100

positive integers? Is there a way to do this quickly with no calculator?

User Amit Bisht
by
7.9k points

1 Answer

7 votes

Final answer:

The mean and median of the first 100 positive integers are both 50.5, resulting in an absolute difference of 0 between them.

Step-by-step explanation:

Calculating the Mean and Median of the First 100 Positive Integers

The mean of the first 100 positive integers can be determined by using the formula for the mean of a series, which is the sum of the integers divided by the number of integers. The sum of the first 100 positive integers is (100/2)*(1+100), which is 5050. This sum divided by 100 gives us a mean of 50.5.

The median is the middle number in a sorted list. Since we have an even number of terms, the median is the average of the 50th and 51st terms. In this series, both of these terms are 50 and 51, so the median is (50+51)/2, which equals 50.5.

Therefore, the absolute difference between the mean and median of the first 100 positive integers is 0 since they are both 50.5.

User Jamie S
by
7.8k points