Dean Chalmers and Julian Gilbey Solutions for Chapter: Representation of Data, Exercise 2: EXERCISE 1A

This stem-and-leaf diagram shows the number of employees at $20$ companies.
$\overline{)\begin{array}{c}1\\ 2\\ 3\end{array}}\begin{array}{cccccccc}0& 8& 8& 8& 8& 9& 9& \\ 0& 5& 6& 6& 7& 7& 8& 9\\ 0& 1& 1& 2& 9& & & \end{array} \begin{array}{c}\mathrm{Key} : \overline{)1} 0\\ \mathrm{represents} 10\\ \mathrm{employees}\end{array}$
What is the most common number of employees?

This stem-and-leaf diagram shows the number of employees at $20$ companies.
$\overline{)\begin{array}{c}1\\ 2\\ 3\end{array}}\begin{array}{cccccccc}0& 8& 8& 8& 8& 9& 9& \\ 0& 5& 6& 6& 7& 7& 8& 9\\ 0& 1& 1& 2& 9& & & \end{array} \begin{array}{c}\mathrm{Key} : \overline{)1} 0\\ \mathrm{represents} 10\\ \mathrm{employees}\end{array}$
How many of the companies have fewer than $25$ employees?

Over a $14$-day period, data were collected on the number of passengers travelling on two ferries, $A$ and $Z.$ The results are presented to the right.
$\begin{array}{rrrrrrrrrr}\begin{array}{}\end{array}& & A& & Z& & & & & \\ 8& 7& 6& \mathbf{2}& & & & & & \\ 7& 6& 4& \mathbf{0}& 3& 0& 5& 8& & \\ 8& 6& 5& \mathbf{3}& 4& 3& 4& 5& 7& 7\\ 5& 3& 3& \mathbf{5}& 0& 2& 6& 6& 9& \end{array}$

Key$:3\left|5\right|0$
Represents $53$ passengers on $A$ and $50$ passengers on $Z$

How many more passengers travelled on ferry $Z$ than on ferry $A?$

The runs scored by two batsmen in 15 cricket matches last season were:
Batsman $P : 53, 41, 57, 38, 41, 37, 59, 48, 52, 39, 47, 36, 37, 44, 59.$
Batsman $Q : 56, 48, 31, 64, 21, 52, 45, 36, 57, 68, 77, 20, 42, 51, 71.$
Giving a reason for your answer, decide which of the batsmen performed more consistently.

The total numbers of eggs laid in the nests of two species of bird were recorded over several breeding seasons.
The numbers of eggs laid in the nests of $10$ wrens and $10$ dunnocks are:
Wrens: $22, 18, 21, 23, 17, 23, 20, 19, 24, 13.$
Dunnocks: $28, 24, 23, 19, 30, 27, 22, 25, 22, 17.$
Represent the data in a back-to-back stem-and-leaf diagram with rows of width $5.$

The total numbers of eggs laid in the nests of two species of bird were recorded over several breeding seasons.
The numbers of eggs laid in the nests of $10$ wrens and $10$ dunnocks are:
Wrens: $22, 18, 21, 23, 17, 23, 20, 19, 24, 13.$
Dunnocks: $28, 24, 23, 19, 30, 27, 22, 25, 22, 17.$
Represent the data in a back-to-back stem-and-leaf diagram with rows of width $5.$

Given that all of these eggs hatched and that the survival rate for dunnock chicks is $92\%,$ estimate the number of dunnock chicks that survived.

The total numbers of eggs laid in the nests of two species of bird were recorded over several breeding seasons.
The numbers of eggs laid in the nests of $10$ wrens and $10$ dunnocks are:
Wrens: $22, 18, 21, 23, 17, 23, 20, 19, 24, 13.$
Dunnocks: $28, 24, 23, 19, 30, 27, 22, 25, 22, 17.$
Represent the data in a back-to-back stem-and-leaf diagram with rows of width $5.$

Find the survival rate for the wren chicks, given that $14$ did not survive.

This back-to-back stem-and-leaf diagram shows the percentage scores of the $25$ students who were the top performers in an examination.
 

$\begin{array}{cll}\text{ Girls (12) }& & \text{ Boys (13) }\\ \begin{array}{cccccc}& & & & 4& 1\\ & & & 8& 6& 6\\ & & 3& 2& 1& 0\\ & & & 8& 7& 7\\ & & & & & \end{array}& \begin{array}{c}8\\ 8\\ 9\\ 9\\ \end{array}& \begin{array}{cccccc}2& & & & & \\ 5& 9& & & & \\ 0& 1& 3& 3& 4& 4\\ 5& 6& 6& 9& & \\ & & & & & \end{array}\end{array}$

Key $:1\mathbf{\left|}8\mathbf{\right|}2$ represents $81\%$ for a girl and $82\%$ for a boy
The $25$ students are arranged in a line in the order of their scores. Describe the student in the middle of the line and find the greatest possible number of boys in the line who are not standing next to a girl.