What is the mean of first 99 natural numbers?a)100b)50.5c)50d)99Correc...
Suppose there are ‘n’ observations {x
1, x
2, x
3,…, x
n}
Calculation:
To find: Mean of the first 99 natural numbers
As we know, Sum of first n natural numbers =
What is the mean of first 99 natural numbers?a)100b)50.5c)50d)99Correc...
Mean is a measure of central tendency that represents the average value of a set of numbers. To find the mean of the first 99 natural numbers, we need to add up all the numbers and then divide by the total count.
Finding the sum of the first 99 natural numbers:
We can use the formula for the sum of an arithmetic series to find the sum of the first 99 natural numbers. The formula is given by:
Sum = (n/2)(first term + last term)
In this case, the first term is 1 and the last term is 99. Therefore, the sum of the first 99 natural numbers is:
Sum = (99/2)(1 + 99) = 99(100)/2 = 9900/2 = 4950
Finding the mean:
To find the mean, we divide the sum of the numbers by the total count, which in this case is 99.
Mean = Sum/Count = 4950/99 = 50
Therefore, the mean of the first 99 natural numbers is 50.
Explanation:
The mean represents the average value of a set of numbers. In this case, we are finding the mean of the first 99 natural numbers. Since the natural numbers are consecutive integers starting from 1, the sum of these numbers will form an arithmetic series. By using the formula for the sum of an arithmetic series, we find that the sum of the first 99 natural numbers is 4950. Dividing this sum by the total count of numbers (99), we find that the mean is 50. This means that if we were to distribute the sum equally among the 99 numbers, each number would have a value of 50. Hence, option C, 50, is the correct answer.