Average of all prime numbers between 30 to 50

Options

A. 37
B. `37.8`
C. 39
D. `39.8`

Answer

To find the average of all prime numbers between 30 and 50, we will follow these steps:

### Step 1: Identify the prime numbers between 30 and 50.
Prime numbers are numbers greater than 1 that have no divisors other than 1 and themselves. The prime numbers between 30 and 50 are:
- 31
- 37
- 41
- 43
- 47

### Step 2: Count the number of prime numbers.
From the list, we can see that there are 5 prime numbers: 31, 37, 41, 43, and 47.

### Step 3: Calculate the sum of the prime numbers.
Now, we will add these prime numbers together:
\[ 31 + 37 + 41 + 43 + 47 \]
Calculating step by step:
- \(31 + 37 = 68\)
- \(68 + 41 = 109\)
- \(109 + 43 = 152\)
- \(152 + 47 = 199\)

So, the total sum of the prime numbers is 199.

### Step 4: Calculate the average.
The average is calculated by dividing the sum of the numbers by the count of the numbers. Here, we divide the sum (199) by the number of prime numbers (5):
\[ \text{Average} = \frac{\text{Sum of prime numbers}}{\text{Number of prime numbers}} = \frac{199}{5} \]
Now, performing the division:
- \(199 \div 5 = 39.8\)

### Final Answer:
The average of all prime numbers between 30 and 50 is **39.8**.

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