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What is the average of all the natural numbers from 1 to 59?
29.5
31
30.5
30
30
For a series of natural numbers starting from 1, the average is simply the sum of the first and last terms divided by two, or specifically for 1 to n, the average is (n+1)/2.
The range of natural numbers is from 1 to 59 inclusive.
Average=2First+LastтАЛ
For a series of natural numbers starting from 1, the average is simply the sum of the first and last terms divided by two, or specifically for 1 to n, the average is (n+1)/2.
Many students try to calculate the sum of all numbers first using n(n+1)/2 and then divide by 59; while correct, it is slower and prone to arithmetic errors.
Identify the range
The set of numbers is {1, 2, 3,..., 59}. This is an arithmetic progression with a common difference of 1.
n=59
Apply Average Formula
For any arithmetic progression, the average is the mean of the first and last terms.
Average=21+59тАЛ
Calculate result
Sum the terms and divide by 2.
Average=260тАЛ=30
D is correct because the average of natural numbers from 1 to 59 is calculated as (1+59)/2, which equals 30.
This concept is a foundational building block for 'Data Interpretation' and 'Statistics' questions involving mean calculations in competitive exams.
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