The average of 17 numbers is 48. The average of first 9 numbers is 45 and…

Given:

• Average of 17 numbers = 48

• Average of first 9 numbers = 45

• Average of next 9 numbers = 52

Note:
The 9th number is common in both groups.
Step 1: Find total sum of 17 numbers
Total sum:
= 17 × 48
= 816
Step 2: Find sums of the two groups
Sum of first 9 numbers:
= 9 × 45
= 405
Sum of next 9 numbers:
= 9 × 52
= 468
Combined sum:
= 405 + 468
= 873
Step 3: Find the 9th number
The 9th number has been counted twice.
Therefore,
9th number:
= 873 − 816
= 57
Step 4: Find average after excluding 9th number
Remaining sum:
= 816 − 57
= 759
Remaining numbers:
= 16
Required average:
= 759/16
= 47.4375