For the calculations of mode of a grouped data,the maximum frequency of a class is denoted by $\ldots \ldots \ldots . .$

In the formula $Z = l + \left( \frac{f_{1} - f_{0}}{2f_{1} - f_{0} - f_{2}} \right) \times c$ for the mode,$f_{2} = \ldots \ldots \ldots$

For the calculation of mode of the following frequency distribution,$f_{1} = \dots \dots \dots \dots \dots \dots$

Class	$0-100$	$100-200$	$200-300$	$300-400$	$400-500$	$500-600$
Frequency	$12$	$18$	$27$	$20$	$17$	$6$

$A$ student noted the number of cars passing through a spot on a road for $100$ periods each of $3\, \text{minutes}$ and summarized it in the table given below. Find the mode of the data:

Number of cars	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$
Frequency	$7$	$14$	$13$	$12$	$20$	$11$	$15$	$8$

Find the mode of the following frequency distribution:

Class	$20-30$	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$	$80-90$
Frequency	$8$	$12$	$27$	$43$	$55$	$37$	$18$

The mode of the following frequency distribution is $37$. Find the missing frequency $x$.

Class	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$	$60-70$
Frequency	$4$	$7$	$x$	$18$	$15$	$8$	$7$