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

Time $\left(xs\right)$	$13.6⩽x<15.4$	$15.4⩽x<17.4$	$17.4⩽x<19.8$
No. adults $\left(f\right)$	$a$	$b$	$27$

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 an estimate of the mean of $x$ and of $y$ given in the following tables.

The following table summarises the number of tomatoes produced by the plants in the plots on a farm.

The tomatoes are weighed accurately and their mean mass is found to be $156.50$ grams. At market they are sold for $\$3.20$ per kilogram and the total revenue is $\$50350.$ Find the actual mean number of tomatoes produced per plot.

All the interior angles of $n$ triangular metal plates, denoted by $y°,$ are measured. State the number of angles measured and write down the value of $\overline{y}.$

The total mass of gold extracted from a mine is denoted by $\Sigma x,$ which is measured in grams. Find an expression in $x$ for the total mass in:

carats, given that $1$ carat is equivalent to $200$ milligrams

The wind speeds, $x$ miles per hour $\left(\mathrm{mph}\right)$, were measured at a coastal location at midday on $40$ consecutive days and are presented in the following table.

Abel wishes to calculate an estimate of the mean wind speed in kilometres per hour $\left(\mathrm{km}/\mathrm{h}\right).$ He knows that a distance of $5$ miles is approximately equal to $8 \mathrm{km}.$

Use the wind speeds in mph to estimate the mean wind speed in $\mathrm{km}/\mathrm{h}.$

What feature of the data suggests that $\overline{t}$ is less than the median? Confirm whether or not this is the case

The following graph illustrates the times taken by $112$ people to complete a puzzle.

Estimate the median time taken.