To find the median and mean of the dataset \( 16, 27, 24, 13, 15, 2, 50 \), we will follow these steps:
Step 1: Sort the data
First, let's sort the data in ascending order:
\[ 2, 13, 15, 16, 24, 27, 50 \]
Step 2: Find the median
The median is the middle value of a data set. For a dataset with an odd number of observations, the median is the value at the position \( \frac{n+1}{2} \), where \( n \) is the number of observations.
Here, we have \( n = 7 \) (since there are 7 numbers).
\[ \text{Median position} = \frac{7 + 1}{2} = 4 \]
The 4th number in the sorted list is \( 16 \).
Thus, the median is 16.
Step 3: Calculate the mean
The mean is calculated by summing all the numbers and then dividing by the total number of observations:
\[ \text{Sum} = 2 + 13 + 15 + 16 + 24 + 27 + 50 = 147 \]
Now, divide the sum by the number of observations:
\[ \text{Mean} = \frac{147}{7} = 21 \]
Thus, the mean is 21.
Summary
- Median: 16
- Mean: 21
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