Find the mean and median of all the positive factors of 72.

Answer

To find the mean and median of all the positive factors of 72, we will follow these steps:

### Step 1: Find the positive factors of 72.
To find the factors, we need to identify all the numbers that can divide 72 without leaving a remainder.

The positive factors of 72 are:
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.

### Step 2: Calculate the mean.
The mean is calculated by taking the sum of all observations (factors) and dividing it by the number of observations.

1. **Sum of the factors**:
\[ 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 18 + 24 + 36 + 72 = 195 \]

2. **Number of factors**:
There are a total of 12 factors.

3. **Mean calculation**:
\[ \text{Mean} = \frac{\text{Sum of factors}}{\text{Number of factors}} = \frac{195}{12} = 16.25 \]

### Step 3: Calculate the median.
The median is the middle value of a data set when it is arranged in ascending order. If there is an even number of observations, the median is the average of the two middle numbers.

1. **Arrange the factors in ascending order** (already done):
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.

2. **Identify the middle values**:
Since there are 12 factors (an even number), the median will be the average of the 6th and 7th values.
- 6th value: 8
- 7th value: 9

3. **Median calculation**:
\[ \text{Median} = \frac{8 + 9}{2} = \frac{17}{2} = 8.5 \]

### Final Answers:
- Mean = 16.25
- Median = 8.5

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