Question

Find the median and mean of the data set 40,4,12,15,45,16

Answer 1

To calculate the median and mean of the data set \(40, 4, 12, 15, 45, 16\), we can follow these steps:

### Step 1: Order the Data

First, we need to arrange the data in ascending order:

\[ 4, 12, 15, 16, 40, 45 \]

### Step 2: Calculate the Median

Since there are an even number of data points (6 data points), the median will be the average of the two middle numbers. The two middle numbers in this ordered list are \(15\) and \(16\).

To find the median:

\[
\text{Median} = \frac{15 + 16}{2} = \frac{31}{2} = 15.5
\]

### Step 3: Calculate the Mean

The mean is calculated by taking the sum of all the data points and dividing by the number of data points.

First, we calculate the sum:

\[
4 + 12 + 15 + 16 + 40 + 45 = 132
\]

Next, we divide the sum by the number of data points:

\[
\text{Mean} = \frac{132}{6} = 22
\]

### Summary

- **Median:** \(15.5\)
- **Mean:** \(22\)