Q&A for How to Calculate Average or Mean of Consecutive Numbers

The average of any five consecutive odd numbers is the third number of the sequence (in this case, c). You can prove this by setting a equal to c-4, b = c-2, d= c+2, and e= c+4. Add those four numbers together with c, and the sum of the five numbers is 5c. Divide that sum by 5 to get the average of the five numbers, which is c.

There are no eight consecutive even numbers (integers) whose average is 8.

Subtract 17,390 from 18,190.

The average (62 in this case) of an odd number of consecutive numbers is the middle number of the set. That means this set begins at four even numbers below 62 and ends at four even numbers above 62. Therefore, the lowest number in this set is 54. You can check this answer by adding together the even numbers from 54 to 70 and then dividing that sum by 9, which yields 62.

Add those numbers and divide by 21.

The mean of a, b, c, d is the same as the mean of m and d, which is (m + d) / 2.

By inspection, it's obvious the middle number is 4. However, if you want to approach this question algebraically, let x be the first number. Then the other two numbers are (x+1) and (x+2). The mean of the three numbers is [(x) + (x+1) + (x+2)] / 3 = (3x + 3) / 3 = 4. Then 3x + 3 = 12, and 3x = 9. That means x = 3, and the middle number is (x+1) = 4.

There are no four consecutive integers that have a mean of 6. If you're not restricted to consecutive integers, you could pick any four numbers that add up to 24. There are many such sets. One example is 3, 4, 8 and 9.