The average of 20 numbers is 227 and the average of other 30 numbers is 120. Find the average of all the numbers taken together.

To find the average of all the numbers taken together, you need to find the total sum of all the numbers and then divide it by the total count of the numbers.

Step 1: Find the total sum of the first set of numbers. The average of the first set of 20 numbers is 227. So, the total sum of these numbers is 20 * 227 = 4540.

Step 2: Find the total sum of the second set of numbers. The average of the second set of 30 numbers is 120. So, the total sum of these numbers is 30 * 120 = 3600.

Step 3: Find the total sum of all the numbers. The total sum of all the numbers is the sum of the total of the first set and the total of the second set. So, the total sum is 4540 + 3600 = 8140.

Step 4: Find the total count of all the numbers. The total count of all the numbers is the sum of the count of the first set and the count of the second set. So, the total count is 20 + 30 = 50.

Step 5: Find the average of all the numbers. The average of all the numbers is the total sum divided by the total count. So, the average is 8140 / 50 = 162.8.