Find the median and mean of the data set below:25, comma, 47, comma, 36, comma, 4825,47,36,48

1. Break Down the Problem

We need to find both the median and the mean of the given data set: $25, 47, 36, 48$.

2. Relevant Concepts

• Median: The median is the middle value of a data set when it is ordered from least to greatest. If there is an even number of observations, the median is the average of the two middle numbers.
• Mean: The mean (or average) is calculated by summing all the values and then dividing by the number of values.

3. Analysis and Detail

• Step 1: Organize the Data Set The given data set is $25, 47, 36, 48$. Arranging it in order gives: $25, 36, 47, 48$

• Step 2: Find the Median Since there are 4 numbers (even), the median will be the average of the 2nd and 3rd values: $\text{Median} = \frac{36 + 47}{2} = \frac{83}{2} = 41.5$

• Step 3: Find the Mean $\text{Mean} = \frac{25 + 36 + 47 + 48}{4} = \frac{156}{4} = 39$

4. Verify and Summarize

• The median calculation checks out, and the data presents no discrepancies.
• Both values calculated (41.5 for median and 39 for mean) are consistent with the definitions.

Final Answer

• Median: $41.5$
• Mean: $39$