Find the modal class for $x$ and for $y$ in the following tables.

$x$	$0-$	$4-$	$14-20$
$f$	$5$	$9$	$8$

 

$y$	$3-6$	$7-11$	$12-20$
$f$	$66$	$80$	$134$

Data about the times, in seconds, taken to run $100$ metres by $n$ adults are given in the following table.

By first investigating the possible values of $a$ and of $b,$ find the largest possible value of $n,$ given that the modal class contains the slowest runners.

Calculate the mean of the following sets of numbers: $28, 16, 83, 72, 105, 55, 6$ and $35$

Calculate the mean of the following sets of numbers:

$7.3, 8.6, 11.7, 9.1, 1.7$ and $4.2$

Calculate the mean of the following sets of numbers:

$3\frac{1}{2}, 5\frac{1}{4}, 9\frac{3}{4},-4\frac{1}{4}$ and $7\frac{3}{8}.$