Question

Find the median and mean of the data set below:
12, comma, 8, comma, 14, comma, 16, comma, 49, comma, 26, comma, 50
12,8,14,16,49,26,50

Answer 1

To find the median and mean of the data set \(12, 8, 14, 16, 49, 26, 50\), we will first sort the numbers in ascending order, then calculate the median and mean.

### Step 1: Sort the Data Set
The sorted data set is:
\[ 8, 12, 14, 16, 26, 49, 50 \]

### Step 2: Find the Median
The median is the middle value of the data set. Since there are 7 numbers (an odd number), the median will be the value at the \((n + 1)/2\) position, where \(n\) is the number of data points.

\[
n = 7 \quad \Rightarrow \quad \text{Median position} = \frac{7 + 1}{2} = 4
\]

The 4th number in the sorted list is \(16\).

**Median = 16**

### Step 3: Find the Mean
The mean is calculated by summing all the numbers and dividing by the count of the numbers.

\[
\text{Sum} = 8 + 12 + 14 + 16 + 26 + 49 + 50 = 175
\]

Now, divide the sum by the number of data points:

\[
\text{Mean} = \frac{\text{Sum}}{n} = \frac{175}{7} = 25
\]

### Final Results
- **Median**: 16
- **Mean**: 25