A survey was conducted to find out the number of books read by students in a class. The frequency distribution of this data is given as follows:\n\nNumber of books: $[0,1,2,3,4,5]$\nFrequency: $[5,10,7,5,2,1]$\n\nFind the variance of the frequency table.

Step 1 ：First, we calculate the mean ($\mu$) of the frequency distribution, which is the sum of the products of each value and its frequency, divided by the total frequency.\n\n$$\mu =\frac{\sum x\ast f}{\sum f}$$\n\nSubstituting the given values:\n\n$$\mu =\frac{(0\ast 5)+(1\ast 10)+(2\ast 7)+(3\ast 5)+(4\ast 2)+(5\ast 1)}{5+10+7+5+2+1}=\frac{50}{30}=1.67$$

Step 2 ：Next, we calculate the variance (${\sigma }^2$), which is the sum of the product of the square of the difference between each value and the mean, times its frequency, divided by the total frequency.\n\n$${\sigma }^2=\frac{\sum (x-\mu {)}^2\ast f}{\sum f}$$\n\nSubstituting the values:\n\n$${\sigma }^2=\frac{(0-1.67{)}^2\ast 5+(1-1.67{)}^2\ast 10+(2-1.67{)}^2\ast 7+(3-1.67{)}^2\ast 5+(4-1.67{)}^2\ast 2+(5-1.67{)}^2\ast 1}{30}=\frac{38.89}{30}=1.30$$