A calculated estimate of the mean capacity of $120$ refrigerators stored at a warehouse is $348$ litres. The capacities are given in the following table.

Capacity (litres)	$160-$	$200-$	$320-$	$400-p$
No. refrigerators $\left(f\right)$	$12$	$28$	$48$	$32$

A delivery of $n$ new refrigerators, all with capacities between $200$ and $320$ litres arrives at the warehouse. This causes the mean capacity to decrease by $8$ litres. Find the value of $n$ and state what assumptions you are making in your calculations.

A carpet fitter is employed to fit carpet in each of the $72$ guest bedrooms at a new hotel. The following table shows how many rooms were completed during the first $10$ days of work.

Based on these figures, estimate how many more days it will take to finish the job. What assumptions are you making in your calculations?

In the figure opposite, a square of side $8 \mathrm{cm}$ is joined edge-to-edge to a semicircle, with centre $O . P$ is $2 \mathrm{cm}$ from $O$ on the figure's axis of symmetry.

Points $X$ and $Y$ are fixed but the position of $Z$ is variable on the shape's perimeter.

Find the mean distance from $P$ to $X, Y$ and $Z$ when angle $POZ$ is equal to: $180°$

In the figure opposite, a square of side $8 \mathrm{cm}$ is joined edge-to-edge to a semicircle, with centre $O . P$ is $2 \mathrm{cm}$ from $O$ on the figure's axis of symmetry.

Points $X$ and $Y$ are fixed but the position of $Z$ is variable on the shape's perimeter.

Find the mean distance from $P$ to $X, Y$ and $Z$ when angle $POZ$ is equal to: $135°$

In the figure opposite, a square of side $8 \mathrm{cm}$ is joined edge-to-edge to a semicircle, with centre $O . P$ is $2 \mathrm{cm}$ from $O$ on the figure's axis of symmetry.

Points $X$ and $Y$ are fixed but the position of $Z$ is variable on the shape's perimeter.

Find obtuse angle $POZ,$ so that the mean distance from $P$ to $X, Y$ and $Z$ is identical to the mean distance from $P$ to $X$ and $Y.$

For $10$ values denoted $x,$ it is given that $\overline{x}=7.4.$ Find: $\Sigma x$.

For $10$ values denoted $x,$ it is given that $\overline{x}=7.4.$ Find: $\Sigma \left(x+2\right)$.

For $10$ values denoted $x,$ it is given that $\overline{x}=7.4.$ Find:

$\Sigma \left(x-1\right)$