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Solution (By Examveda Team)

Understanding the Question:
The question asks for the arithmetic mean (average) of prime numbers from 1 to 19.

What are Prime Numbers?
Prime numbers are numbers greater than 1 that have only two factors: 1 and themselves.
Examples: 2, 3, 5, 7, 11, etc.

Step 1: Identify the Prime Numbers between 1 and 19
The prime numbers in this range are: 2, 3, 5, 7, 11, 13, 17, 19.

Step 2: Calculate the Sum of the Prime Numbers
Add all the prime numbers together: 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 = 77.

Step 3: Count the Number of Prime Numbers
We identified 8 prime numbers.

Step 4: Calculate the Arithmetic Mean (Average)
Divide the sum of the prime numbers (77) by the number of prime numbers (8): 77 / 8 = 9.625.

Step 5: Round to Two Decimal Places
Rounding 9.625 to two decimal places gives 9.63.

Therefore, the answer is Option D: 9.63