Dean Chalmers and Julian Gilbey Solutions for Chapter: Measures of Central Tendency, Exercise 6: EXERCISE 2C

The SD card slots on digital cameras are designed to accommodate a card of up to $24 \mathrm{mm}$ in width. Due to low sales figures, a manufacturer suspects that the machine used to cut the cards needs to be recalibrated. The widths, $w \mathrm{mm},$ of $400$ of these cards were measured and are coded in the following table, where $x=w-24.$

What percentage of the SD cards are too wide to fit into the slots?

The SD card slots on digital cameras are designed to accommodate a card of up to $24 \mathrm{mm}$ in width. Due to low sales figures, a manufacturer suspects that the machine used to cut the cards needs to be recalibrated. The widths, $w \mathrm{mm},$ of $400$ of these cards were measured and are coded in the following table, where $x=w-24.$

Use the coded data to estimate the mean width of these $400$ cards.

Sixteen bank accounts have been accidentally under-credited by the following amounts, denoted by $\$x.$

$\begin{array}{llllllll}917.95& 917.98& 918.03& 917.97& 918.01& 917.94& 918.05& 918.07\\ 918.02& 917.93& 918.01& 917.88& 918.10& 917.85& 918.11& 917.94\end{array}$

To calculate $\overline{x}$ manually, Fidel and Ramon code these figures using $\left(x-917\right)$ and $\left(x-920\right),$ respectively.

Who has the simpler maths to do? Explain your answer.

Throughout her career, an athlete has been timed in $120$ of her $400$-metre races. Her times, denoted by $t$ seconds, were recorded on indoor tracks $45$ times and are summarised by $\Sigma \left(t-60\right)=83.7,$ and on outdoor tracks where $\Sigma \left(t-65\right)=-38.7$ Calculate her average $400$-metre running time and comment on the accuracy of your answer.

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 $\overline{y}.$

All the interior angles of $n$ triangular metal plates, denoted by $y°,$ are measured. Hence, or otherwise, find the value of $\Sigma \left(y-30\right).$

A dataset of $20$ values is denoted by $x$ where $\Sigma \left(x-1\right)=58.$ Another dataset of $30$ values is denoted by $y$ where $\Sigma \left(y-2\right)=36.$ Find the mean of the $50$ values of $x$ and $y.$

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.