Question

Find the median and mean of the data set below:
16, comma, 27, comma, 24, comma, 13, comma, 15, comma, 2, comma, 50
16,27,24,13,15,2,50
Answer

Answer 1

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