Question

Find the median and mean of the data set below:
20,43,39,45,38,45,8

Answer 1

To find the median and mean of the data set \(20, 43, 39, 45, 38, 45, 8\), we will follow these steps:

### Step 1: Finding the Median

1. **Sort the data set in ascending order**:
\[
8, 20, 38, 39, 43, 45, 45
\]

2. **Determine the number of data points**:
There are 7 data points (an odd number).

3. **Find the middle value**:
The median is the value at position \((n + 1)/2\), where \(n\) is the number of data points.
\[
(7 + 1)/2 = 8/2 = 4
\]
The median is the 4th number in the sorted list:
\[
\text{Median} = 39
\]

### Step 2: Finding the Mean

1. **Sum all the data points**:
\[
8 + 20 + 38 + 39 + 43 + 45 + 45 = 238
\]

2. **Divide the sum by the number of data points**:
\[
\text{Mean} = \frac{238}{7} \approx 34
\]

### Final Results
- **Median**: \(39\)
- **Mean**: \(\approx 34\)