The average of 19 numbers is 42. The average of the first 6 numbers is 38.5 and that of the last 14 numbers is 45.5. If the sixth number is excluded then what’s the average of the remaining numbers? (Correct to one decimal place)

Step 1: Calculate the total sum of the 19 numbers. The average is 42, so the total sum is 42 * 19 = 798.

Step 2: Calculate the total sum of the first 6 numbers. The average is 38.5, so the total sum is 38.5 * 6 = 231.

Step 3: Calculate the total sum of the last 14 numbers. The average is 45.5, so the total sum is 45.5 * 14 = 637.

Step 4: Notice that the sixth number is counted twice in the above calculations (once in the first 6 numbers and once in the last 14 numbers). So, subtract the total sum of the 19 numbers from the sum of the first 6 numbers and the last 14 numbers to find the sixth number. The sixth number is 231 + 637 - 798 = 70.

Step 5: Now, exclude the sixth number from the total sum of the 19 numbers to find the sum of the remaining 18 numbers. The sum of the remaining 18 numbers is 798 - 70 = 728.

Step 6: Finally, calculate the average of the remaining 18 numbers by dividing the sum by the number of numbers. The average is 728 / 18 = 40.4 (correct to one decimal place).