State advantages of diagram types

7 The heights, in cm, of the 11 basketball players in each of two clubs, the Amazons and the Giants, are shown below.

1. State an advantage of using a stem-and-leaf diagram compared to a box-and-whisker plot to illustrate this information.
2. Represent the data by drawing a back-to-back stem-and-leaf diagram with Amazons on the left-hand side of the diagram.
3. Find the interquartile range of the heights of the players in the Amazons.
   Four new players join the Amazons. The mean height of the 15 players in the Amazons in now 191.2 cm . The heights of three of the new players are \(180 \mathrm {~cm} , 185 \mathrm {~cm}\) and 190 cm .
4. Find the height of the fourth new player.
   If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.

6 A box of biscuits contains 30 biscuits, some of which are wrapped in gold foil and some of which are unwrapped. Some of the biscuits are chocolate-covered. 12 biscuits are wrapped in gold foil, and of these biscuits, 7 are chocolate-covered. There are 17 chocolate-covered biscuits in total.

1. Copy and complete the table below to show the number of biscuits in each category.

   	Wrapped in gold foil	Unwrapped	Total
   Chocolate-covered
   Not chocolate-covered
   Total			30

   A biscuit is selected at random from the box.
2. Find the probability that the biscuit is wrapped in gold foil. The biscuit is returned to the box. An unwrapped biscuit is then selected at random from the box.
3. Find the probability that the biscuit is chocolate-covered. The biscuit is returned to the box. A biscuit is then selected at random from the box.
4. Find the probability that the biscuit is unwrapped, given that it is chocolate-covered. The biscuit is returned to the box. Nasir then takes 4 biscuits without replacement from the box.
5. Find the probability that he takes exactly 2 wrapped biscuits.

1 Ashfaq and Kuljit have done a school statistics project on the prices of a particular model of headphones for MP3 players. Ashfaq collected prices from 21 shops. Kuljit used the internet to collect prices from 163 websites.

1. Name a suitable statistical diagram for Ashfaq to represent his data, together with a reason for choosing this particular diagram.
2. Name a suitable statistical diagram for Kuljit to represent her data, together with a reason for choosing this particular diagram.

6

1. Give one advantage and one disadvantage of using a box-and-whisker plot to represent a set of data.
2. The times in minutes taken to run a marathon were recorded for a group of 13 marathon runners and were found to be as follows. $$\begin{array} { l l l l l l l l l l l l l } 180 & 275 & 235 & 242 & 311 & 194 & 246 & 229 & 238 & 768 & 332 & 227 & 228 \end{array}$$ State which of the mean, mode or median is most suitable as a measure of central tendency for these times. Explain why the other measures are less suitable.
3. Another group of 33 people ran the same marathon and their times in minutes were as follows.

   190	203	215	246	249	253	255	254	258	260	261
   263	267	269	274	276	280	288	283	287	294	300
   307	318	327	331	336	345	351	353	360	368	375

   (a) On the grid below, draw a box-and-whisker plot to illustrate the times for these 33 people.
   \includegraphics[max width=\textwidth, alt={}, center]{f4d040a2-6a04-49ce-98ac-8ba5c515f905-09_611_1202_1270_555}
   (b) Find the interquartile range of these times.

1 A study of the ages of car drivers in a certain country produced the results shown in the table. \begin{table}[h] \end{table} Illustrate these results diagrammatically.

1 The weights of 30 children in a class, to the nearest kilogram, were as follows. Construct a grouped frequency table for these data such that there are five equal class intervals with the first class having a lower boundary of 41.5 kg and the fifth class having an upper boundary of 61.5 kg .

10 Jane conducted a survey. She chose a sample of people from three towns, A, B and C. She noted the following information. 400 people were chosen.
230 people were adults.
55 adults were from town A .
65 children were from town A .
35 children were from town B .
150 people were from town B .

1. In the Printed Answer Booklet, complete the two-way frequency table.

   \multirow{2}{*}{}	Town
   	A	B	C	Total
   adult
   child
   Total

2. One of the people is chosen at random.
   1. Find the probability that this person is an adult from town A .
   2. Given that the person is from town A , find the probability that the person is an adult. For another survey, Jane wanted to choose a random sample from the 820 students living in a particular hostel. She numbered the students from 1 to 820 and then generated some random numbers on her calculator. The random numbers were 0.114287562 and 0.081859817 . Jane's friend Kareem used these figures to write down the following sample of five student numbers. 114, 142, 428, 287 and 756 Jane used the same figures to write down the following sample of five student numbers.
      114, 287, 562, 81 and 817
3. 1. State, with a reason, which one of these samples is not random.
   2. Explain why Jane omitted the number 859 from her sample.

7 The pre-release material contains information about health expenditure. Fig. 7.1 shows an extract from the data. \begin{table}[h] \end{table}

1. Explain how the data should be cleaned before any analysis takes place. Kareem uses all the available data to conduct an investigation into health expenditure as a percentage of GDP in different countries. He calculates the mean to be 6.79 and the standard deviation to be 2.78 . Fig. 7.2 shows the smallest values and the largest values of health expenditure as a percentage of GDP. \begin{table}[h]

   Smallest values of Health expenditure (\% of GDP)	Largest values of Health expenditure (\% of GDP)
   1.5	11.7
   1.9	11.9
   2.1	13.7
   	13.7
   	16.5
   	17.1
   	17.1

   \captionsetup{labelformat=empty} \caption{Fig. 7.2}
   \end{table}
2. Determine which of these values are outliers. Kareem removes the outliers from the data and finds that there are 187 values left. He decides to collect a sample of size 30 . He uses the following sampling procedure.
   Assign each value a number from 1 to 187. Generate a random number, \(n\), between 1 and 13 . Starting with the \(n\)th value, choose every 6th value after that until 30 values have been chosen.
3. Explain whether Kareem is using simple random sampling.

9 Fig. 9.1 shows box and whisker diagrams which summarise the birth rates per 1000 people for all the countries in three of the regions as given in the pre-release data set.
The diagrams were drawn as part of an investigation comparing birth rates in different regions of the world. Africa (Sub-Saharan)
\includegraphics[max width=\textwidth, alt={}, center]{05376a51-e768-4b45-9c18-c98255a4bd70-08_104_991_557_730} East and South East Asia
\includegraphics[max width=\textwidth, alt={}, center]{05376a51-e768-4b45-9c18-c98255a4bd70-08_109_757_744_671} Caribbean
\includegraphics[max width=\textwidth, alt={}, center]{05376a51-e768-4b45-9c18-c98255a4bd70-08_99_369_982_730} \begin{figure}[h] \end{figure}

1. Discuss the distributions of birth rates in these regions of the world. Make three different statements. You should refer to both information from the box and whisker diagrams and your knowledge of the large data set.
2. The birth rates for all the countries in Australasia are shown below.

   Country	Birth rate per 1000
   Australia	12.19
   New Zealand	13.4
   Papua New Guinea	24.89

   1. Explain why the calculation below is not a correct method for finding the birth rate per 1000 for Australasia as a whole. $$\frac { 12.19 + 13.4 + 24.89 } { 3 } \approx 16.83$$
   2. Without doing any calculations, explain whether the birth rate per 1000 for Australasia as a whole is higher or lower than 16.83 . The scatter diagram in Fig. 9.2 shows birth rate per 1000 and physicians/ 1000 population for all the countries in the pre-release data set. \begin{figure}[h]
      \includegraphics[alt={},max width=\textwidth]{05376a51-e768-4b45-9c18-c98255a4bd70-09_898_1698_386_274} \captionsetup{labelformat=empty} \caption{Fig. 9.2}
      \end{figure}
3. Describe the correlation in the scatter diagram.
4. Discuss briefly whether the scatter diagram shows that high birth rates would be reduced by increasing the number of physicians in a country.

1. (a) Describe the main features and uses of a box plot.
   

Children from schools \(A\) and \(B\) took part in a fun run for charity. The times, to the nearest minute, taken by the children from school \(A\) are summarised in Figure 1. \begin{figure}[h] \end{figure} (b) (i) Write down the time by which \(75 \%\) of the children in school \(A\) had completed the run.
(ii) State the name given to this value.
(c) Explain what you understand by the two crosses ( X ) on Figure 1.
For school \(B\) the least time taken by any of the children was 25 minutes and the longest time was 55 minutes. The three quartiles were 30,37 and 50 respectively.
(d) Draw a box plot to represent the data from school \(B\).
\includegraphics[max width=\textwidth, alt={}, center]{c8bade79-a39a-4055-bfae-928f5338fdfc-03_798_1196_580_372}
(e) Compare and contrast these two box plots.

13
12

1. 
   Using the box plot, give one comparison of central tendency and one comparison of spread for the two regions.
   [0pt] [2 marks]
   Comparison of central tendency
   Comparison of spread \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\)
   \end{tabular}}}
   \hline & & &
   \hline \end{tabular} \end{center} 12
2. Jaspal, an environmental researcher, used all of the data in the Large Data Set to produce a statistical comparison of the \(\mathrm { CO } _ { 2 }\) and CO emissions in regions of England. Using your knowledge of the Large Data Set, give two reasons why his conclusions may be invalid.