To find the median and mean of the data set \(20, 4, 17, 44, 48, 29\), we can follow these steps:
Step 1: Organize the data
First, we should sort the data in ascending order:
\[ 4, 17, 20, 29, 44, 48 \]
Step 2: Find the median
The median is the middle value of a data set. Since there are 6 numbers (an even number), the median will be the average of the two middle numbers.
The two middle numbers are the 3rd and 4th values in the sorted list:
- 3rd value: \(20\)
- 4th value: \(29\)
Now, calculate the average:
\[ \text{Median} = \frac{20 + 29}{2} = \frac{49}{2} = 24.5 \]
Step 3: Find the mean
The mean is calculated by adding all the numbers together and then dividing by the count of numbers.
Sum of the numbers:
\[ 4 + 17 + 20 + 29 + 44 + 48 = 162 \]
Count of numbers: \(6\)
Now, calculate the mean:
\[ \text{Mean} = \frac{162}{6} = 27 \]
Final Results
- Median: \(24.5\)
- Mean: \(27\)