Dean Chalmers and Julian Gilbey Solutions for Chapter: Measures of Variation, Exercise 11: EXERCISE 3E

Building plots are offered for sale at $\$315$ per square metre. The seller has to pay a lawyer's fee of $\$500$ from the money received. Salome's plot is $240$ square metres larger than Nadia's plot. How much more did the seller receive from Salome than from Nadia after paying the lawyer's fees?

Temperatures in degrees Celsius $\left({}^{\circ }\mathrm{C}\right)$ can be converted to temperatures in degrees Fahrenheit $\left({}^{\circ }\mathrm{F}\right)$ using the formula $F=1.8C+32.$

The temperatures yesterday had a range of $15°\mathrm{C}.$ Express this range in degrees Fahrenheit.

Temperatures in degrees Celsius $\left({}^{\circ }\mathrm{C}\right)$ can be converted to temperatures in degrees Fahrenheit $\left({}^{\circ }\mathrm{F}\right)$ using the formula $F=1.8C+32.$

Temperatures elsewhere were recorded at hourly intervals in degrees Fahrenheit and were found to have mean $54.5$ and variance $65.61.$ Find the mean and standard deviation of these temperatures in degrees Celsius.

Ten items were selected from each of four sections at a supermarket. Details of the prices of those items, in dollars, on$1\mathrm{st}$ April and on $1\mathrm{st}$ June are shown in the following table.

For which section's items the following statements be true? Briefly explain your answers.

The total cost of the items did not change.

Ten items were selected from each of four sections at a supermarket. Details of the prices of those items, in dollars, on$1\mathrm{st}$ April and on $1\mathrm{st}$ June are shown in the following table.

For which section's items could each of the following statements be true? Briefly explain each of your answers.

The price of each item changed by the same amount.

Ten items were selected from each of four sections at a supermarket. Details of the prices of those items, in dollars, on$1\mathrm{st}$ April and on $1\mathrm{st}$ June are shown in the following table.

For which section's items could each of the following statements be true? Briefly explain each of your answers.

The proportional change in the price of each item was the same.

The lengths of $45$ ropes used at an outdoor recreational centre can be extended by $30\%$ when stretched. The sum of the squares of their stretched lengths is $0.0507{ \mathrm{km}}^2$ and their natural lengths, $x$ metres, are summarised by $\Sigma {\left(x-20\right)}^2=1200.$ Find the mean natural length of these $45$ ropes.

Over a short period of time in $2016,$ the value of the pound sterling $\left(\pounds \right)$ fell by $15.25\%$ against the euro $\left(€\right).$ Find the percentage change in the value of the euro against the pound over this same period.