Question

Find the median and mean of the data set below:
3
5
6
16
49

Answer 1

To find the median and mean of the given data set \( \{3, 5, 6, 16, 49\} \), we can follow these steps:

### Step 1: Finding the Median
The median is the middle value of a data set when it is ordered from least to greatest.

1. **Order the data set**:
- The data set is already ordered as \( 3, 5, 6, 16, 49 \).

2. **Identify the middle value**:
- Since there are 5 numbers (an odd number of observations), the median will be the middle number, which is the 3rd number in the ordered list.

Thus, the median is **6**.

### Step 2: Finding the Mean
The mean is calculated by taking the sum of all the numbers and dividing it by the total number of observations.

1. **Calculate the sum**:
\[
3 + 5 + 6 + 16 + 49 = 79
\]

2. **Count the total number of observations**:
- There are 5 numbers in the data set.

3. **Calculate the mean**:
\[
\text{Mean} = \frac{\text{Sum}}{\text{Number of observations}} = \frac{79}{5} = 15.8
\]

### Summary
- **Median**: 6
- **Mean**: 15.8