Students investigated the prices in dollars $\left(\$\right)$ of $1$ litre bottles of a certain drink at $24$ shops in a town and at $16$ shops in surrounding villages. Denoting the town prices by $t$ and the village prices by $v,$ the students' data are summarised by the totals $\Sigma \left(t-1.1\right)=1.44$ and $\Sigma \left(v-1.2\right)=0.56.$

Find the mean price of $1$ litre of this drink at all the shops at which the students collected their data.

The masses, $x \mathrm{kg},$ of $12$ objects are such that $\overline{x}=0.475.$ Find the value of $\Sigma 1000x$ and state what it represents.

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

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 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:

kilograms.

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 $8 \mathrm{km}.$

Explain how Abel can calculate his estimate without converting the given boundary values from miles per hour to kilometres per hour.

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 $\mathrm{km}/\mathrm{h}.$

Given that $15$ values of $x$ are such that $\Sigma \left(3x-2\right)=528,$ find $\overline{x}$ and find the value of $b$ such that $\Sigma \left(0.5x-b\right)=138.$