Answer:
Value of the sixth number = 42
Explanation:
Step 1: Find the mean of the five numbers:
Before we can find the value of the sixth number, we'll first need to find the mean of the five numbers.
The mean is defined as the sum of a set of values divided by the total number of values.
Since there are five numbers, dividing the sum of these numbers by 5 will give us the mean:
Mean = (3 + 16 + 9 + 38 + 24) / 5
Mean = (90) / 5
Mean = 18
Thus, the mean of the five numbers is 18.
Step 2: Find the value of the sixth number:
We can let n represent the sixth number. Because we're told that the mean of the set of six numbers is 4 more than the mean of the set of five numbers, we can use the following equation to find n, the value of the sixth number:
(3 + 16 + 9 + 38 + 4 + n) / 6 = 18 + 4
(90 + n) / 6 = 22
90 + n = 132
n = 42
If you plug in 42 for n, you get a mean of 22 since (3 + 16 + 9 + 38 + 4 + 42) / 6 simplifies first to 132 / 6 and then to 22.
22 is indeed 4 more than 18 (i.e., the mean of the set of five numbers).