find the average of all odd natural numbers , well as that of all the even natural numbers , less than 20 compare the two averages
well, geez, one way is just to find the average of each set:
(1+3+5+7+9+11+13+15+17+19)/10 = ____
(2+4+6+8+10+12+14+16+18)/9 = _____
Now just do your comparison.
a more elegant way, also suitable for a much larger set of values, makes use of the fact that the sum of the first n odd numbers is n^2.
So, the sum of the first 10 odd numbers is 10^2
Since even numbers are all multiples of 2, the sum of the first n even numbers is two times the sum of the numbers 1..n
Now , the sum of the numbers from 1 to n is n(n+1)/2
So, the sum of the first 9 even numbers is 9*10
really good smart work
To find the average of all odd natural numbers less than 20, we first need to list them:
1, 3, 5, 7, 9, 11, 13, 15, 17, 19.
To calculate the average, we add up all the numbers and divide by the total count:
(1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19) / 10 = 98 / 10 = 9.8.
So, the average of all odd natural numbers less than 20 is 9.8.
Now let's find the average of all even natural numbers less than 20:
2, 4, 6, 8, 10, 12, 14, 16, 18.
Following the same calculation, we add up these numbers and divide by the total count:
(2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18) / 9 = 90 / 9 = 10.
Therefore, the average of all even natural numbers less than 20 is 10.
Comparing the two averages, we can see that the average of odd natural numbers (9.8) is smaller than the average of even natural numbers (10).
To find the average of a set of numbers, you need to sum all the numbers and then divide by the total count of numbers.
Let's start by finding the average of all odd natural numbers less than 20:
Odd natural numbers less than 20: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19
To find the sum, add up all the numbers:
1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 = 100
Next, determine the count of odd numbers, which is 10.
Now, find the average by dividing the sum by the count:
Average of odd numbers = 100 / 10 = 10
Similarly, let's find the average of all even natural numbers less than 20:
Even natural numbers less than 20: 2, 4, 6, 8, 10, 12, 14, 16, 18
To find the sum, add up all the numbers:
2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 = 90
Next, determine the count of even numbers, which is also 9.
Find the average by dividing the sum by the count:
Average of even numbers = 90 / 9 = 10
Now, let's compare the two averages:
The average of odd numbers is 10, while the average of even numbers is also 10. Therefore, the two averages are equal.
In conclusion, the average of all odd natural numbers less than 20 is 10, and the average of all even natural numbers less than 20 is also 10.