Given below is the data of the ages of various children.

What is the difference between the mean and mode of the ages?

$$arithmetic\ mean=\frac{\left(Sum\ of\ the\ ages\ of\ the\ number\ of\ children\right)}{number\ of\ children}$$

= $$\frac{17\times6+16\times7+16\times8+17\times9+19\times10+15\times11}{17+16+16+17+19+15}$$

= $$\frac{102+112+128+153+190+165}{100}$$

= $$\frac{850}{100}$$

= 8.5

Mode = the highest number of children having a age = 10 (Here 19 children has 10 years of age.)

difference between the mean and mode of the ages = 10-8.5 = 1.5