Dean Chalmers and Julian Gilbey Solutions for Chapter: Measures of Central Tendency, Exercise 5: EXERCISE 2B

Twenty boys and girls were each asked how many aunts and uncles they have. The entry $4/5$ in the following table, for example, shows that $4$ boys and $5$ girls each have $3$ aunts and $2$ uncles.

For the boys and girls together, calculate the mean number of aunts.

Twenty boys and girls were each asked how many aunts and uncles they have. The entry $4/5$ in the following table, for example, shows that $4$ boys and $5$ girls each have $3$ aunts and $2$ uncles.

For the boys and girls together, calculate the mean number of aunts and uncles.

Twenty boys and girls were each asked how many aunts and uncles they have. The entry $4/5$ in the following table, for example, shows that $4$ boys and $5$ girls each have $3$ aunts and $2$ uncles.

Suggest an alternative way of presenting the data so that the calculations in parts $a$ and $b$ would be simpler to make.

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.

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 $Y.$