Dean Chalmers and Julian Gilbey Solutions for Chapter: Representation of Data, Exercise 10: END-OF-CHAPTER REVIEW EXERCISE 1

The weights of $220$ sausages are summarised in the following table.

State how many sausages weighed between $50 \mathrm{g}$ and $60 \mathrm{g}$.

The capacities of ten engines, in litres, are given rounded to 2 decimal places, as follows: 

$1.86,2.07,1.74,1.08,1.99,1.96,1.83,1.45,1.28$ and $2.19$.  

These capacities are to be grouped in three classes as $1.0-1.4,1.5-2.0$ and $2.1-2.2$

.Find the frequency of the class $1.5-2.0$ litres.

Over a $10$-day period, Alina recorded the number of text messages she received each day. The following stem-and-leaf diagram shows her results.

$$\begin{gathered} \begin{array}{lllllll}\mathbf{0}& 9& & & & & \\ \mathbf{1}& 0& 3& 4& 4& & \\ \mathbf{1}& 5& 5& 5& 6 8& & \end{array} \\ \mathrm{Key}: \mathbf{1}\mid 5 \\ \mathrm{represents} 15 \mathrm{messages} \end{gathered}$$

On how many days did she receive more than $10$ but not more than $15$ messages?

Eighty people downloaded a particular application and recorded the time taken for the download to complete. The times are given in the following table.

Find the number of downloads that completed in $5$ to $6$ minutes.

The histograms below illustrate the number of hours of sunshine during August in two regions, $A$ and $B$. Neither region had more than 8 hours of sunshine per day.

After studying the histograms, two students make the following statements.

- Bindu: There was more sunshine in region A than in region$B$ during the first$2$ weeks of August.
- Janet: In August there was less sunshine in region $A$ than in region $B$.
Discuss these statements and decide whether or not you agree with each of them.In each case, explain your reasoning.

A hotel has $90$ rooms. The table summarises information about the number of rooms occupied each day for a period of $200$days.

Draw a cumulative frequency graph on graph paper to illustrate this information.

A hotel has $90$ rooms. The table summarises information about the number of rooms occupied each day for a period of $200$days.

Draw a cumulative frequency graph on graph paper to illustrate this information.

Estimate the number of days when more than $30$ rooms were occupied.

A hotel has $90$ rooms. The table summarises information about the number of rooms occupied each day for a period of $200$days.

Draw a cumulative frequency graph on graph paper to illustrate this information.

On $75\%$ of the days at most $n$ rooms were occupied. Estimate the value of$n$.