To find the median and mean of the data set [tex]\( 20, 4, 17, 44, 48, 29 \)[/tex], we follow these steps:
### Mean Calculation:
1. Sum all the numbers in the dataset:
[tex]\[ 20 + 4 + 17 + 44 + 48 + 29 = 162 \][/tex]
2. Count the numbers in the dataset:
The dataset has six numbers.
3. Divide the sum by the count of numbers:
[tex]\[ \text{Mean} = \frac{162}{6} = 27.0 \][/tex]
### Median Calculation:
1. Sort the dataset in ascending order:
[tex]\[ 4, 17, 20, 29, 44, 48 \][/tex]
2. Determine the middle numbers in the sorted dataset:
Since there are six numbers (an even number of elements), the median is the average of the third and fourth numbers.
3. Identify the third and fourth numbers:
The third number is [tex]\( 20 \)[/tex] and the fourth number is [tex]\( 29 \)[/tex].
4. Calculate the average of these two numbers:
[tex]\[ \text{Median} = \frac{20 + 29}{2} = \frac{49}{2} = 24.5 \][/tex]
Therefore, the median is [tex]\( 24.5 \)[/tex] and the mean is [tex]\( 27.0 \)[/tex].
### Final Answer:
Median [tex]\( = 24.5 \)[/tex]
Mean [tex]\( = 27.0 \)[/tex]
