Construct back-to-back stem-and-leaf from raw data

6 The annual salaries, in thousands of dollars, for 11 employees at each of two companies \(A\) and \(B\) are shown below.

1. Represent the data by drawing a back-to-back stem-and-leaf diagram with company \(A\) on the left-hand side of the diagram.
2. Find the median and the interquartile range of the salaries of the employees in company \(A\). [3]
   A new employee joins company \(B\). The mean salary of the 12 employees is now \(
   ) 38500$.
3. Find the salary of the new employee.

5 The following table gives the weekly snowfall, in centimetres, for 11 weeks in 2018 at two ski resorts, Dados and Linva.

1. Represent the information in a back-to-back stem-and-leaf diagram.
2. Find the median and the interquartile range for the weekly snowfall in Dados.
3. The median, lower quartile and upper quartile of the weekly snowfall for Linva are 12, 9 and 32 cm respectively. Use this information and your answers to part (b) to compare the central tendency and the spread of the weekly snowfall in Dados and Linva.

2 Lakeview and Riverside are two schools. The pupils at both schools took part in a competition to see how far they could throw a ball. The distances thrown, to the nearest metre, by 11 pupils from each school are shown in the following table.

1. Draw a back-to-back stem-and-leaf diagram to represent this information, with Lakeview on the left-hand side.
2. Find the interquartile range of the distances thrown by the 11 pupils at Lakeview school.

3 The Lions and the Tigers are two basketball clubs. The heights, in cm, of the 11 players in each of their first team squads are given in the table.

1. Draw a back-to-back stem-and-leaf diagram to represent this information, with the Lions on the left.
2. Find the median and the interquartile range of the heights of the Lions first team squad.
   It is given that for the Tigers, the lower quartile is 183 cm , the median is 190 cm and the upper quartile is 195 cm .
3. Make two comparisons between the heights of the players in the Lions first team squad and the heights of the players in the Tigers first team squad.

4 The heights, in cm, of the 11 players in each of two teams, the Aces and the Jets, are shown in the following table.

1. Draw a back-to-back stem-and-leaf diagram to represent this information with the Aces on the left-hand side of the diagram.
2. Find the median and the interquartile range of the heights of the players in the Aces.
3. Give one comment comparing the spread of the heights of the Aces with the spread of the heights of the Jets.

6 Teams of 15 runners took part in a charity run last Saturday. The times taken, in minutes, to complete the course by the runners from the Falcons and the runners from the Kites are shown in the table.

1. Draw a back-to-back stem-and-leaf diagram to represent this information, with the Falcons on the left-hand side.
2. Find the median and the interquartile range of the times for the Falcons.
   Let \(x\) and \(y\) denote the times, in minutes, of a runner from the Falcons and a runner from the Kites respectively. It is given that $$\sum x = 792 , \quad \sum x ^ { 2 } = 43504 , \quad \sum y = 783 , \quad \sum y ^ { 2 } = 42223 .$$
3. Find the mean and the standard deviation of the times taken by all 30 runners from the two teams.

5 The lengths of the diagonals in metres of the 9 most popular flat screen TVs and the 9 most popular conventional TVs are shown below.

1. Represent this information on a back-to-back stem-and-leaf diagram.
2. Find the median and the interquartile range of the lengths of the diagonals of the 9 conventional TVs.
3. Find the mean and standard deviation of the lengths of the diagonals of the 9 flat screen TVs.

5 The following are the maximum daily wind speeds in kilometres per hour for the first two weeks in April for two towns, Bronlea and Rogate.

1. Draw a back-to-back stem-and-leaf diagram to represent this information.
2. Write down the median of the maximum wind speeds for Bronlea and find the interquartile range for Rogate.
3. Use your diagram to make one comparison between the maximum wind speeds in the two towns.

7 The times in minutes taken by 13 pupils at each of two schools in a cross-country race are recorded in the table below.

1. Draw a back-to-back stem-and-leaf diagram to illustrate these times with Thaters School on the left.
2. Find the interquartile range of the times for pupils at Thaters School.
   The times taken by pupils at Whitefay Park School are denoted by \(x\) minutes.
3. Find the value of \(\Sigma ( x - 60 ) ^ { 2 }\).
4. It is given that \(\Sigma ( x - 60 ) = 46\). Use this result, together with your answer to part (iii), to find the variance of \(x\).
   If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.

4 The weights in kilograms of 11 bags of sugar and 7 bags of flour are as follows.
Sugar: 1.9611 .98312 .00812 .0141 .9681 .9941 .2 .0112 .0171 .9771 .9841 .989
Flour: \(\begin{array} { l l l l l l l } 1.945 & 1.962 & 1.949 & 1.977 & 1.964 & 1.941 & 1.953 \end{array}\)

1. Represent this information on a back-to-back stem-and-leaf diagram with sugar on the left-hand side.
2. Find the median and interquartile range of the weights of the bags of sugar.

5 The weights, in kilograms, of the 15 rugby players in each of two teams, \(A\) and \(B\), are shown below.

1. Represent the data by drawing a back-to-back stem-and-leaf diagram with team \(A\) on the lefthand side of the diagram and team \(B\) on the right-hand side.
2. Find the interquartile range of the weights of the players in team \(A\).
3. A new player joins team \(B\) as a substitute. The mean weight of the 16 players in team \(B\) is now 93.9 kg . Find the weight of the new player.

7 The masses, in grams, of components made in factory \(A\) and components made in factory \(B\) are shown below.

1. Draw a back-to-back stem-and-leaf diagram to represent the masses of components made in the two factories.
2. Find the median and the interquartile range for the masses of components made in factory \(B\).
3. Make two comparisons between the masses of components made in factory \(A\) and the masses of those made in factory \(B\).

7 The heights, in cm, of the 11 members of the Anvils athletics team and the 11 members of the Brecons swimming team are shown below.

1. Draw a back-to-back stem-and-leaf diagram to represent this information, with Anvils on the left-hand side of the diagram and Brecons on the right-hand side.
2. Find the median and the interquartile range for the heights of the Anvils.
   The heights of the 11 members of the Anvils are denoted by \(x \mathrm {~cm}\). It is given that \(\Sigma x = 1923\) and \(\Sigma x ^ { 2 } = 337221\). The Anvils are joined by 3 new members whose heights are \(166 \mathrm {~cm} , 172 \mathrm {~cm}\) and 182 cm .
3. Find the standard deviation of the heights of all 14 members of the Anvils.
   If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.