Find the mean of :
(i) The first eight natural numbers
(ii) the first ten odd numbers
(iii) the frist seven multiples of `5.`
(iv) all the factors of `20`
(v) all prime numbers between `50` and `80.`

Explanation

To find the mean for each of the given sets of numbers, we will follow the formula for mean:

\[ \text{Mean} = \frac{\text{Sum of observations}}{\text{Total number of observations}} \]

Let's solve each part step by step.

### (i) The first eight natural numbers
1. **Identify the first eight natural numbers**: The first eight natural numbers are 1, 2, 3, 4, 5, 6, 7, 8.
2. **Calculate the sum**:
\[ \text{Sum} = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36 \]
3. **Count the total number of observations**: There are 8 natural numbers.
4. **Calculate the mean**:
\[ \text{Mean} = \frac{36}{8} = 4.5 \]

### (ii) The first ten odd numbers
1. **Identify the first ten odd numbers**: The first ten odd numbers are 1, 3, 5, 7, 9, 11, 13, 15, 17, 19.
2. **Calculate the sum**:
\[ \text{Sum} = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 = 100 \]
3. **Count the total number of observations**: There are 10 odd numbers.
4. **Calculate the mean**:
\[ \text{Mean} = \frac{100}{10} = 10 \]

### (iii) The first seven multiples of 5
1. **Identify the first seven multiples of 5**: The first seven multiples of 5 are 5, 10, 15, 20, 25, 30, 35.
2. **Calculate the sum**:
\[ \text{Sum} = 5 + 10 + 15 + 20 + 25 + 30 + 35 = 140 \]
3. **Count the total number of observations**: There are 7 multiples of 5.
4. **Calculate the mean**:
\[ \text{Mean} = \frac{140}{7} = 20 \]

### (iv) All the factors of 20
1. **Identify the factors of 20**: The factors of 20 are 1, 2, 4, 5, 10, 20.
2. **Calculate the sum**:
\[ \text{Sum} = 1 + 2 + 4 + 5 + 10 + 20 = 42 \]
3. **Count the total number of observations**: There are 6 factors of 20.
4. **Calculate the mean**:
\[ \text{Mean} = \frac{42}{6} = 7 \]

### (v) All prime numbers between 50 and 80
1. **Identify the prime numbers between 50 and 80**: The prime numbers are 53, 59, 61, 67, 71, 73, 79.
2. **Calculate the sum**:
\[ \text{Sum} = 53 + 59 + 61 + 67 + 71 + 73 + 79 = 463 \]
3. **Count the total number of observations**: There are 7 prime numbers.
4. **Calculate the mean**:
\[ \text{Mean} = \frac{463}{7} \approx 66.14 \]

### Summary of Results
- (i) Mean of the first eight natural numbers: **4.5**
- (ii) Mean of the first ten odd numbers: **10**
- (iii) Mean of the first seven multiples of 5: **20**
- (iv) Mean of all factors of 20: **7**
- (v) Mean of all prime numbers between 50 and 80: **66.14**