Final answer:
The overall average of the ten numbers, which includes four numbers averaging 21 and six numbers averaging 27, is calculated to be 24.6.
Step-by-step explanation:
To find the overall average of the ten numbers, we can use the information provided about the average of the first 4 numbers and the average of the next 6 numbers.
The calculation for the overall average requires the sum of all ten numbers divided by ten. The sum for the first 4 numbers is 4 times their average, which is 4 × 21 = 84. Similarly, the sum for the next 6 numbers is 6 × 27 = 162. Combining these sums gives us a total of 84 + 162 = 246.
To find the overall average, we divide the total sum by the number of values, which is 10 in this case:
Overall Average = 246 / 10 = 24.6.
So, the overall average of the ten numbers is 24.6.