What is the difference between the mean and median of the given data:
4, 6, 3, 7, 10, 13, 16 and 5?

$$Mean=\frac{sum\ of\ data}{number\ of\ data}$$

$$=\frac{4+6+3+7+10+13+16+5}{8}$$

$$=\frac{64}{8}$$

= 8

For median, first we need to arrange the given data in ascending order from left to right.

3, 4, 5, 6, 7, 10, 13, 16

n = number of data = 8

median = $$\frac{\left(\frac{n}{2}\right)^{th}\ term\ +\ \left(\frac{n}{2}+1\right)^{th}\ term}{2}$$

= $$\frac{\left(\frac{8}{2}\right)^{th}\ term\ +\ \left(\frac{8}{2}+1\right)^{th}\ term}{2}$$

= $$\frac{4^{th}\ term\ +\ \left(4+1\right)^{th}\ term}{2}$$

= $$\frac{4^{th}\ term\ +\ 5^{th}\ term}{2}$$

= $$\frac{6+7}{2}$$

= $$\frac{13}{2}$$

= 6.5

difference between the mean and median = 8-6.5

= 1.5