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The Robert Smyth School Mathematics Faculty Topic 2a Specify, Plan & Collect Data Innovation & excellence Name: HW1 – Grade C Analysing questionnaires 1. A survey is to be carried out to investigate the shopping habits of the population of a town. (a) Give two reasons why the survey should not be carried out between 9am and 5pm on a Wednesday. Reason 1 ..................................................................................................................... Teacher Assessment ..................................................................................................................................... ..................................................................................................................................... Reason 2 ..................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (2) (b) Write two suitable questions that could be asked in the survey. Question 1 .................................................................................................................. ..................................................................................................................................... ..................................................................................................................................... Question 2 .................................................................................................................. ..................................................................................................................................... ..................................................................................................................................... (2) (Total 4 marks) 2. Mandip is doing a survey on “Healthy Eating” in the town where he lives. (a) Give one reason why he should not do the survey outside the sports centre. ..................................................................................................................................... ..................................................................................................................................... (1) (b) One of the questions he asks is “Do you eat fruit or sweets?” Explain why this is a poorly worded question. ..................................................................................................................................... ..................................................................................................................................... (1) The Robert Smyth School 1 The Robert Smyth School Mathematics Faculty Topic 2a Specify, Plan & Collect Data Innovation & excellence (c) There are 2000 people in the town where Mandip lives. He interviews 15 people for his survey. Explain why his survey may not be representative of the people in the town. ..................................................................................................................................... ..................................................................................................................................... (1) (Total 3 marks) 3. The manager of Cost-U-Less supermarket wants to carry out a survey of her customers. She asks customers to complete a questionnaire. (a) Here is one of the questions she asks: “Don’t you agree that Cost-U-Less is the best supermarket?” Write down one criticism of this question. ...................................................................................................................................... ...................................................................................................................................... ...................................................................................................................................... (1) (b) Here is another part of her questionnaire. Question How much do you spend at Cost-U-Less? Response (tick one box) Under £10 Under £20 Under £50 Under £100 Write down one criticism of the question and one criticism of the response section. Criticism of question ................................................................................................... ...................................................................................................................................... ...................................................................................................................................... Criticism of response section ....................................................................................... ...................................................................................................................................... ...................................................................................................................................... (2) The Robert Smyth School 2 The Robert Smyth School Mathematics Faculty Topic 2a Specify, Plan & Collect Data Innovation & excellence (c) The manager collects her data by asking 100 shoppers who visit the supermarket on Friday evening. Explain why this sample may not be representative of all the shoppers who use this supermarket. ...................................................................................................................................... ...................................................................................................................................... ...................................................................................................................................... ...................................................................................................................................... (1) (d) The manager wants to find out how often shoppers use this supermarket. Write a question that the manager could ask. Include a response section. Question ...................................................................................................................... ...................................................................................................................................... ...................................................................................................................................... Response (2) (Total 6 marks) 4. Nadia delivers a questionnaire to every house on her street. One of the questions on the questionnaire is “Do you agree that under-16s should not be allowed outdoors after 9 pm?” (a) (i) Write down one criticism of this question. ........................................................................................................................... ........................................................................................................................... (1) The Robert Smyth School 3 The Robert Smyth School Mathematics Faculty Topic 2a Specify, Plan & Collect Data Innovation & excellence (ii) Explain why Nadia’s method of collecting data is not suitable. ........................................................................................................................... ........................................................................................................................... (1) (b) Write a suitable question asking parents what they think is the latest time that under-16s should be indoors. Include a response section. ...................................................................................................................................... ...................................................................................................................................... ...................................................................................................................................... ...................................................................................................................................... ...................................................................................................................................... ...................................................................................................................................... (2) (Total 4 marks) Success: The Robert Smyth School Target: 4 The Robert Smyth School Mathematics Faculty Topic 2a Specify, Plan & Collect Data Innovation & excellence HW2 – Grade C Analysing and designing two way tables 1. Karin is collecting data about the number of brothers and the number of sisters of the people in her class. Teacher Karin’s results are given in the two-way table. Assessment Number of brothers Number of sisters (a) 0 1 2 3 0 6 7 1 2 1 4 3 0 1 2 1 2 1 0 3 1 1 0 0 How many people have one brother? ..................................................................................................................................... Answer ..................................................... (2) (b) How many people have more brothers than sisters? ..................................................................................................................................... ..................................................................................................................................... Answer ..................................................... (2) (c) There are 30 people in Karin’s class. What is the probability that a randomly chosen person from her class has the same number of brothers and sisters? ..................................................................................................................................... Answer ..................................................... (2) (Total 6 marks) 2. Here is a pack of ten cards. The Robert Smyth School 5 The Robert Smyth School Mathematics Faculty Topic 2a Specify, Plan & Collect Data Innovation & excellence (a) Complete this two-way table to show the number of different cards in the pack. Shaded Unshaded Circles Triangles (2) (b) One of the cards is picked at random. What is the probability that it has either a shaded circle or an unshaded triangle? ..................................................................................................................................... Answer............................................................................... (2) (Total 4 marks) 3. Jane conducts a survey of the favourite colours of the students in her class. She records the results. Male Red Female Yellow Male Green Male Yellow Female Red Male Yellow Male Red Female Green Male Green Female Green Female Green Female Red Male Record the results in a two-way table. (Total 3 marks) 4. Emma reads in a magazine that there is a link between the number of children and the number of pets in a family. (a) Design a two-way table to record the number of pets and the number of children in a sample of families. (3) (b) Complete your two-way table by inventing data for eight families. Success: The Robert Smyth School (1)(Total 4 marks) Target: 6 Red The Robert Smyth School Mathematics Faculty Topic 2a Specify, Plan & Collect Data Innovation & excellence HW3 – Grade A/B Random sampling and stratified samples 1. The manager of a cinema wants to find out how often teenagers attend the cinema. Teacher assessment He uses a questionnaire. (a) Here is one part of the questionnaire. Question How often do you attend the cinema? Response Sometimes Occasionally Regularly Write down two criticisms of his response section. Criticism 1 ................................................................................................................. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... Criticism 2 ................................................................................................................. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (2) (b) Explain how the manager could distribute 50 questionnaires randomly to pupils from a school of 1000 pupils. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (1) (Total 3 marks) The Robert Smyth School 7 The Robert Smyth School Mathematics Faculty Topic 2a Specify, Plan & Collect Data Innovation & excellence 2. (a) Jane stood outside the school library and collected the views of 50 pupils. Explain why her method of obtaining data will not give a random sample. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (1) (b) Sahima decides to take a stratified sample, of 50 pupils, by year group from the 1000 pupils in the school. The table shows the number of pupils in each year group at the school. Year 7 8 9 10 11 Number of pupils 167 200 230 210 193 Calculate the number of pupils that Sahima should choose from each year group. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... Answer Year 7 ........…................................................... Year 8 .......….................................................... Year 9 .......….................................................... Year 10 ............................................................. Year 11 ............................................................. (4) (Total 5 marks) The Robert Smyth School 8 The Robert Smyth School Mathematics Faculty Topic 2a Specify, Plan & Collect Data Innovation & excellence 3. Each day 65 trains pass through Bristol. Of these, 23 go North, 21 go South, 13 go East and 8 go West. For a survey, Paul decides to take a 20% sample of these trains. He plans to choose every fifth train that passes. (a) Explain why the sample obtained may not represent the different routes fairly. .....................………………………………………………………………………… .....................………………………………………………………………………… (1) (b) Paul decides to take a 20% stratified sample. Calculate the number of trains going each way that he should choose. .....................………………………………………………………………………… .....................………………………………………………………………………… .....................………………………………………………………………………… .....................………………………………………………………………………… North: ………, South: ………, East: ………, West:……… (4) (Total 5 marks) 4. Annie wants to choose a sample of people from three neighbouring towns to find out what they think about a plan to close a local hospital. Town A Town C Town B (a) State one advantage of using a sample stratified by town. .....................………………………………………………………………………… .....................………………………………………………………………………… (1) The Robert Smyth School 9 The Robert Smyth School Mathematics Faculty Topic 2a Specify, Plan & Collect Data Innovation & excellence (b) Approximately 20 000 people live in Town A, 5 000 in Town B and 16 000 in Town C. Annie wants a stratified sample of size 100. (i) Show that she should choose 49 people from Town A. ...…………………………………………………………………………........ ...…………………………………………………………………………........ (1) (ii) Calculate how many people she should choose from each of the other towns. ...…………………………………………………………………………........ ...…………………………………………………………………………........ Town B ........……................ Town C ……………………… (2) (Total 4 marks) 5. The table shows the number of boys and the number of girls in each year in a school of 2000 pupils. (a) Year 7 Year 8 Year 9 Year 10 Year 11 Boys 163 186 198 196 187 Girls 201 204 234 218 213 A 10% sample, stratified by year and gender, is needed. Complete the table to show how many boys and how many girls should be chosen from each year. ......................………………………………………………………………………… ......................………………………………………………………………………… Year 7 Year 8 Year 9 Year 10 Year 11 Boys Girls (3) (b) The sample chosen will be asked for their opinions on a number of school related issues. Explain why a stratified sample will be more useful than a random sample. ......................………………………………………………………………………… ......................………………………………………………………………………… ......................………………………………………………………………………… (2) The Robert Smyth School 10 The Robert Smyth School Mathematics Faculty Topic 2a Specify, Plan & Collect Data Innovation & excellence (c) There are 930 boys and 1070 girls in the school altogether. Compare the numbers of children in your sample from part (a) with the numbers that you would have in a 10% sample stratified by gender only. ......................………………………………………………………………………… ......................………………………………………………………………………… ......................………………………………………………………………………… ......................………………………………………………………………………… (2) (Total 7 marks) 6. Mr Singh wants to choose four pupils from a class list to attend a meeting. There are 10 boys and 18 girls in the class. (a) Explain why a stratified sample may be better than a random sample in this situation. ...................................................................................................................................... ...................................................................................................................................... (1) (b) Calculate the number of boys and the number of girls who should be chosen for a stratified sample of four pupils. ...................................................................................................................................... ...................................................................................................................................... Boys ...................... Girls ........................ (2) (c) Explain how Mr Singh should choose the girls to send to the meeting. ...................................................................................................................................... ...................................................................................................................................... ...................................................................................................................................... ...................................................................................................................................... ...................................................................................................................................... (2) (Total 5 marks) Success: The Robert Smyth School Target: 11 The Robert Smyth School Mathematics Faculty Topic 2a Specify, Plan & Collect Data Innovation & excellence HW4 – Grade A*/A/B Teacher assessment Random and stratified samples & National Census 1. 1000 people visit a museum one day. The table shows the number of each type of visitor. Number of children Child Adult Senior Citizen 318 452 230 Peter wants to find out the views of the visitors. He decides to take a stratified sample of 50 visitors. Calculate the number of each type of visitor he should choose. .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. Answer Child ....................................................................... Adult ...................................................................... Senior Citizen ........................................................ (Total 4 marks) 2. A college wants to obtain a sample of its student population. The college decides to take a stratified sample of size 200 by ethnic group. The table shows the student population by ethnic group. (a) Ethnic group Student population White 725 Black 388 Asian 186 Other 151 Show that the college should choose 26 Asian students as part of its sample. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (2) The Robert Smyth School 12 The Robert Smyth School Mathematics Faculty Topic 2a Specify, Plan & Collect Data Innovation & excellence (b) Calculate the number of students that the college should choose from each of the ethnic groups. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... Answer White ............................ Black ............................ Asian ...........26............. Other ............................ (3) (Total 5 marks) 3. A computer is used to generate three-digit random numbers from 000 to 999, e.g. 006, 000, 977, 125, ... Given that a generated number is a multiple of 3, find the probability that it is also a multiple of 4. ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... Answer ……………………………………… (Total 4 marks) The Robert Smyth School 13 The Robert Smyth School Mathematics Faculty Topic 2a Specify, Plan & Collect Data Innovation & excellence 4. The owner of a health club wants to find out how often the members use the club. He first collects data about the age and gender of the 1000 members. (a) Under 25 25 - 40 41 - 50 Over 50 Men 162 265 134 49 Women 178 110 70 32 Give one reason why a stratified sample may be better than a random sample in this situation. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (b) (1) The owner decides to take a stratified sample of size 50 by age and gender. (i) Calculate how many men aged 25-40 he should choose. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... Answer .................................................................. (ii) (2) Calculate how many members of each gender he should choose. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... Answer Men ............................................................................... Women .......................................................................... (2) (Total 5 marks) 5. (a) Explain how you could obtain a random sample of 50 residents from a village. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (1) The Robert Smyth School 14 The Robert Smyth School Mathematics Faculty Topic 2a Specify, Plan & Collect Data Innovation & excellence (b) The population of a town is 61 500. The table below shows the population of the town by age group. Age group Under 18 18 to 35 36 to 65 Over 65 Population 12 100 25 300 16 600 7 500 Calculate the number from each age group that would be needed for a stratified sample of size 1000. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... Answer Under 18 18 to 35 36 to 65 Over 65 (3) (Total 4 marks) 6. (a) What is a National Census? ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (1) (b) According to a National Census, 23% of people are under 21 and 34% of people are over 60. Sally wants to give a questionnaire to a sample of 150 people stratified by age. Use the National Census figures to obtain a stratified sample of size 150. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... Answer Under 21.................................. 21-60……………... Over 60………………… (3) (Total 4 marks) The Robert Smyth School 15 The Robert Smyth School Mathematics Faculty Topic 2a Specify, Plan & Collect Data Innovation & excellence 7. 500 pupils in a boarding school are divided into 3 houses. The number of pupils in each house is shown in the table. House Number of pupils Kingfisher Magpie Blackbird 170 120 210 The headteacher wants to form a council of representatives from each house. (a) The headteacher decides to take a sample of 25 pupils, stratified by house. Calculate the number of pupils chosen from each house. Show your working. ...................................................................................................................................... ...................................................................................................................................... ...................................................................................................................................... Answer Kingfisher ................................................... Magpie ........................................................ Blackbird ..................................................... (3) (b) Explain how the headteacher could choose the pupils from Magpie House. ...................................................................................................................................... ...................................................................................................................................... ...................................................................................................................................... ...................................................................................................................................... (1) (Total 4 marks) Success: The Robert Smyth School Target: 16
