Find the mean of all prime numbers between 20 and 50.

Answer

To find the mean of all prime numbers between 20 and 50, we will follow these steps:

### Step 1: Identify the prime numbers between 20 and 50.
Prime numbers are those that have only two factors: 1 and the number itself. The prime numbers between 20 and 50 are:
- 23
- 29
- 31
- 37
- 41
- 43
- 47

### Step 2: List the prime numbers.
We can write down the identified prime numbers:
- 23, 29, 31, 37, 41, 43, 47

### Step 3: Calculate the sum of these prime numbers.
Now, we will add these numbers together:
\[ 23 + 29 + 31 + 37 + 41 + 43 + 47 \]
Calculating step-by-step:
- \(23 + 29 = 52\)
- \(52 + 31 = 83\)
- \(83 + 37 = 120\)
- \(120 + 41 = 161\)
- \(161 + 43 = 204\)
- \(204 + 47 = 251\)

So, the sum of the prime numbers is \(251\).

### Step 4: Count the total number of prime numbers.
We have identified a total of 7 prime numbers.

### Step 5: Calculate the mean.
The mean is calculated by dividing the sum of the prime numbers by the total count of the prime numbers:
\[ \text{Mean} = \frac{\text{Sum of prime numbers}}{\text{Total number of prime numbers}} = \frac{251}{7} \]
Now, we perform the division:
\[ \frac{251}{7} \approx 35.8571 \]
Rounding this gives us approximately \(35.86\).

### Final Answer:
The mean of all prime numbers between 20 and 50 is approximately \(35.86\).

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