Question

Find the median and mean of the data set below:
11, comma, 6, comma, 37, comma, 34, comma, 7
11,6,37,34,7

Answer 1

To find the median and mean of the data set \(11, 6, 37, 34, 7\), we will first sort the numbers and then calculate each value.

### Step 1: Sort the Data
The sorted data set is:
\[ 6, 7, 11, 34, 37 \]

### Step 2: Find the Median
Since there are 5 numbers (which is odd), the median is the middle number in the sorted list.

The middle position can be found using the formula:
\[
\text{Median position} = \frac{n+1}{2}
\]
where \(n\) is the number of observations. So for our case:
\[
\frac{5 + 1}{2} = 3
\]
The 3rd number in the sorted list is 11.

Thus, the **median** is:
\[
\text{Median} = 11
\]

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

Calculating the sum:
\[
6 + 7 + 11 + 34 + 37 = 95
\]

Now divide by the number of observations (5):
\[
\text{Mean} = \frac{95}{5} = 19
\]

### Summary
- **Median:** 11
- **Mean:** 19