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