If the average of 11 numbers are 20 and the average of 3 numbers are 48, what is the average of all the numbers.(
the total of the first 11 numbers is (11)(20) or 220, and the total of the other 3 numbers is 3(48) or 144
so the total is 220+144 = 364
and there are 14 numbers
the average of all of them is 364/14 = 26
To find the average of all the numbers, we need to consider both sets of numbers together. The total sum of both sets of numbers can be found by multiplying the average of the first set by the number of values in the first set, and then adding it to the product of the average of the second set and the number of values in the second set.
First, let's find the total sum of the first set of numbers. We know that the average of 11 numbers is 20, so the sum of these numbers can be calculated by multiplying the average by the number of values:
Sum of the first set = 20 * 11 = 220
Next, let's find the total sum of the second set of numbers. We know that the average of 3 numbers is 48, so the sum of these numbers can be calculated by multiplying the average by the number of values:
Sum of the second set = 48 * 3 = 144
Now, we can find the average of all the numbers by adding the sums of both sets of numbers and dividing the total sum by the total number of values:
Total sum of all numbers = Sum of the first set + Sum of the second set = 220 + 144 = 364
Total number of values = Number of values in the first set + Number of values in the second set = 11 + 3 = 14
Average of all numbers = Total sum of all numbers / Total number of values = 364 / 14
Therefore, the average of all the numbers is approximately 26.