2.1 Tally charts and frequency tables

Transcription

1 1 Tally charts and frequency tables Objectives Tally raw data using a standard tally chart Construct frequency tables Key words Tally chart Frequency table Cumulative frequency Starter Ask each student how they travelled to school and record the data as a list on the board. Main teaching Show the list of travel to school data on slide 1 of PowerPoint 1A. How many people travelled by bus? How easy was it to answer the question quickly? Discuss why a simple list is inefficient. How could you sort this travel to school list into a more sensible and useable form? Establish that a tally would be useful and demonstrate constructing one using slide Discussion points Why might you use a tally? Why does the table include a frequency column? Why might you be interested in the total frequency? (Number of students who took part) As a class, complete the frequency table on slide 3 with each person s mode of transport to school today. Display slide 1 of PowerPoint 1B and work through the example with students, inviting them to calculate each cumulative frequency before revealing the answer. Tell students they will be working in pairs to construct a data collection sheet to record numbers of brothers and sisters. Collect data from the whole class with students using their own data collection sheets. Students then complete a cumulative frequency table. What information can the cumulative frequency table give which is not easily seen using the frequency table? PowerPoint 1A PowerPoint 1B Links Collecting Data co.uk/hotlinks (code 4554T) ActiveTeach resources MS PowerPoint presentations: 1A Travel to school, and 1B Cumulative frequency Chapter 2 game Follow up sections 1 3 and Exercise 2A sections 4 5 (with PowerPoint 1C), Exercise 2B and Worksheets 1B and 1C section 6 and Exercise 2C Extra practice Worksheet 1A (answers on page 179) Sections

2 PowerPoint 1C Two-way tables This PowerPoint presentation is on the ActiveTeach CD-ROM 36

3 Worksheet 1A Tally charts and frequency tables sections 1 3 This list table below gives the ages of 24 children who attended auditions for a children s TV show Design and complete a frequency table for these data. This list shows the results of a survey to find out the types of pets owned by some children. cat cat dog dog dog fish fish horse bird cat dog dog fish fish fish rabbit bird bird cat dog dog dog fish rabbit bird cat cat dog fish horse rabbit rabbit bird cat dog dog dog fish fish horse Design and complete a frequency table for these data. Write down the name of the pet that was most popular The table shows the numbers of telephone calls received per hour by a call centre over a 24-hour period. 0, 1, 0, 1, 0, 3, 4, 12, 16, 32, 43, 31, 43, 38, 24, 22, 35, 37, 28, 24, 15, 6, 3, 1 Design and complete a grouped frequency table for these data. Use class intervals 0 9, and so on. Add a cumulative frequency column to your table. Write down the number of hours when the centre received less than 10 calls. Write down the number of hours when the centre received more than 20 calls. The judges at a gymnastics competition awarded the following scores to competitors Draw and complete a grouped frequency table for these data. Use class intervals <3, 3 3.4, , and so on. Add a cumulative frequency column to your table. Write down the number of competitors who scored more than

4 Worksheet 1B sections 4 5 Two-way tables Thirty junior members of a sports club school were asked to choose an event in which to compete in a competition. 100 m High jump Total Boys 11 4 Girls 6 Total Copy and complete the two-way table to show how many girls and boys took part in each event. Write down the number of girls who ran in the 100 m race. Fifty people were asked whether they preferred comedy, soaps or sport on television. Men Women Total Comedy 2 7 Soaps 15 Sport Total 50 Copy and complete the table to show the men s and the women s preferences. Write down the total number of people who preferred sport. Work out how many more women were asked their preferences than men. 3. The table shows the distribution of some businesses operating in three towns. Hairdressers Beauty therapists Health stores Total Town A Town B 25 2 Town C 32 Total Copy and complete the table. Write down the number of health stores in Town C. Write down the total number of beauty therapists. Work out how many more hairdressers there are in Town C than in Town A. 38

5 Worksheet 1C sections 4 5 Reading tables The price of renting a holiday home is dependent upon the type of property and the start date of the rental. The prices per week (in pounds) for properties in one holiday resort are shown below. A booking fee of is added to the price of each holiday. Type of property Rental start date A B C D E 2 Oct 8 Oct Oct 15 Oct Oct 29 Oct Oct 17 Dec Dec 24 Dec Dec 31 Dec Jan 4 Feb e) f) g) h) Between which dates can the cheapest holidays be found? Give a reason why holidays may be cheaper at this time. Write down the least amount I could pay for a holiday from this company. Between which dates are the most expensive holidays found? Give a reason that holidays may be more expensive at this time. Write down the type of property that is the most expensive. What would I pay for a week in property type C beginning on 12 th October? Work out the difference in price between property type B and property type E on 21 st December. The table shows the times of trains and fares from London to Birmingham. Time London to Birmingham Dep Arr Ticket Standard First class Advance Any time Off peak 440 Any time Off peak 440 Any time Advance Any time Advance Any time Write down the cost, the ticket type and the train for the cheapest travel from London to Birmingham. I need to be in Birmingham at 5.30 pm. Which is the latest train I can catch? Work out the difference in price between an Any time First class ticket and an Advance Standard ticket for the train from London to Birmingham. 39

6 7 Pictorial representation Objectives Starter Display slide 1 of PowerPoint 7A. The picture shows different breakfast cereals but it does not convey information. How many packets of Choc Corn were sold? The picture doesn t give us that information. Main teaching The pictogram on slide 2 shows information about the quantity of different boxes of cereal sold by a small shop. How would you complete the pictogram to show 40 packets of Corn Crunch were sold? Discussion points Which was the most popular breakfast cereal? How many packets of breakfast cereal were sold altogether? What does 1 symbol represent? Talk through the key points relating to pictograms on slide 3. Tell students that they are going to construct pictograms for the travel to school data they collected in lesson (If these data aren t available carry out a quick survey to find out how each student in the class travelled to school this morning.) Use slide 4 to discuss which symbols would be easy to divide up into different quantities. Then discuss what symbol they might choose and what one symbol will represent. Students should construct their pictograms on squared or graph paper. Remind them that Present data in a clear and interesting way Use symbols to represent a number of items all symbols must be the same size the spacing between symbols must be even they must include a key. Key words Pictogram Key Resources Squared paper or graph paper Links Creating and interpreting pictograms www. heinemann.co.uk/ hotlinks (code 4554T) ActiveTeach resources MS PowerPoint presentation 7A Pictorial representation Chapter 2 game Follow up sections 7 8 and Exercise 2D sections 9 10 (with PowerPoint 7B Bar charts and line graphs), Exercise 2E and Worksheets 7B and 7C Extra practice Worksheet 7A (answers on page 179) Sections

7 PowerPoint 7B Bar charts and vertical line graphs This PowerPoint presentation is on the ActiveTeach CD-ROM 41

8 Worksheet 7A sections 7 8 Pictograms The frequency table below shows the number of tins of each type of soup sold by a corner shop in one week. Flavour Number of tins Chicken 65 Tomato 50 Vegetable 45 Mushroom 20 Minestrone 30 Beef 35 Draw a pictogram to display this information. Tip: Use a rectangle for the picture. Remember to include a key. All members of an athletics club took part in a survey to find which sports they take part in. The pictogram shows the results of the survey. Jumping Throwing Running (track) Running (long distance) Mixed (decathlon etc.) Key 5 members Write down the sport that was the most popular. Write down the sport that was the least popular. Work out the number of people who took part in running (track). Work out how many people took part in the survey. 42

9 Worksheet 7B section 9 Bar charts A transport authority conducted a survey of 50 cars in a town centre. The number of occupants of each car was recorded. The results are shown in the frequency table. Number of occupants Frequency More than 5 1 Draw a bar chart to show this information. The bar chart shows the scores obtained when a six-sided dice was rolled. Frequency Number on dice Write down the number that was rolled most frequently. Write down the number that was rolled least frequently. Work out how many times the dice was rolled. Write down whether or not you think this was a fair dice. 43

10 Worksheet 7C section 10 Vertical line graphs The vertical line graph shows the number of certain animals in the Kids Zone at a small zoo. Frequency Rabbits Hamsters Goats Lambs Chickens Donkeys Write down the number of rabbits in the Kids Zone. Write down the most common animal in the Kids Zone. There are 2 donkeys. Copy and complete the graph to show the donkeys. Work out how many animals there are altogether. The table shows the number of students studying diploma courses at a sixth form college. Diploma Number of students Engineering 41 Health and social care 43 Hair and beauty 56 Creative and media 72 Information technology 65 Construction 37 Show this information on a vertical line graph. 44

11 11 Stem and leaf diagrams Objective Draw and interpret stem and leaf diagrams Starter Who has dates in their pockets? Ask students to take any coins out of their pockets and look carefully for the date on each one. Each student should count the total number of coins they have. The dates will be needed later. Main teaching Display the data on slide 1 of PowerPoint 11A, which shows the numbers of coins that students in a class had in their pockets. Explain to students that a stem and leaf diagram is one way of arranging and displaying these data. Work through the stages of slide 1, which shows how to construct a stem and leaf diagram. Stress the need for a key. Once the stem and leaf diagram is complete, check the students understanding of the diagram. What was the smallest number of coins? What was the largest? What is the advantage of a stem and leaf diagram? Discuss the advantage of a stem and leaf diagram. (It allows you to see the value of each individual piece of data over bar charts or vertical line graphs, which only give the shape of the distribution.) How does a stem and leaf diagram show the shape of the distribution? Ask approximately 12 students to write the number of coins in their pocket on the board. Work together as a class to create a stem and leaf diagram for these data on slide Key words Stem and leaf diagram Key Resources Coins in students pockets Links Stem and leaf diagram examples co.uk/hotlinks (code 4554T) ActiveTeach resources MS PowerPoint presentation 11A Stem and leaf diagrams Chapter 2 game Follow up section 12 (with PowerPoint 11B), Exercise 2G and Worksheet 11B section 13 and Worksheet 11C section 14 (with PowerPoint 11C) and Worksheet 11D Extra practice Worksheet 11A (answers on page 180) Sections

12 PowerPoint 11B Pie charts These PowerPoint presentations are on the ActiveTeach CD-ROM PowerPoint 11C Cumulative step polygons 46

13 Worksheet 11A section 11 Stem and leaf diagrams During an experiment a boy measured the height (to the nearest centimetre) of some plants after 30 days growth. His results are shown below Draw an ordered stem and leaf diagram for these data. Write down the most common height for the plants. Should the plant that measured 0 cm be included? Give a reason for your answer. Write down the height of the tallest plant measured. A salesman recorded the distances, in miles, he travelled from London to the places he visited in June on the stem and leaf diagram below Key 1 28 means 128 miles from London Work out the number of places he visited altogether. The furthest place he visited was Inverness. Write down how far this is from London. The shortest distance he travelled was to Rochester. Write down how far this is from London. On every journey he has to go there and back again. Work out the range of distances travelled. e) Work out the total distance travelled during June. 47

14 Worksheet 11B section 12 Pie charts A local authority has produced a pie chart to show where the money in its budget comes from. Business Rates Where the money comes from Housing Rents Government Grants Council Tax Sales of Goods and Services Where does the largest proportion of the money come from? What angle represents the money that comes from Council Tax? What angle represents the money that comes from Sale of Goods and Services? The council raised 120 million from Council Tax. Work out how much it raised altogether. The way the council spends the money received on services is shown in the table. Services on which money is spent million Administration 60 Housing 75 Children and Education 210 Roads 45 Adult Social Care 90 Work out how much money is spent altogether. A pie chart is to be drawn to show how the money is spent. Work out the angle that would represent administration. Show your working. Draw the pie chart to show how the money is spent. 48

15 Worksheet 11C Advantages and disadvantages of diagrams section Write down two advantages of using a bar chart to display data. Write down two advantages of using a stem and leaf diagram to display data. Write down one disadvantage of using a pie chart to display data. James collects some data. He records the number of siblings each member of his class has. He decides to use a pie chart to display the data. This is not the best choice. Write down the name of a better diagram to use and give a reason for your choice. A company is producing different diagrams to display data for different clients. bar chart vertical line graph pictogram pie chart stem and leaf diagram For each set of data below choose which diagram listed above would be the best choice to display the data. Give a reason for your answer. The amount of rain that fell daily during August in a holiday resort. Which animals could be seen in a zoo. The marks scored by individual competitors in a gymnastics competition. The different types of rubbish which are recycled by a local authority. e) The cost of staying in hotels in different cities. f) The different kinds of fish caught in a trawler s nets. g) The daily hours of sunshine in a town. h) The approximate attendance at 5 football matches. i) The proportion of different crops grown on a farm. 49

16 Worksheet 11D Cumulative frequency step polygons section 14 Copy and complete the following cumulative frequency table. Matches played Frequency Cumulative frequency The frequency table gives the numbers of goals scored by football teams one weekend. Goals Frequency Cumulative frequency Copy and complete the cumulative frequency table for these data. Write down how many teams took part altogether. Draw a cumulative frequency step polygon for these data. How many teams scored fewer than 2 goals? 3. The frequency table gives the cost and number of second class packages sent from a post office on one day. Stamps Frequency Cumulative frequency 95p p p p p 10 e) Copy and complete the cumulative frequency table for these data. Write down the total number of packages sent. Draw a cumulative frequency step polygon for these data. How many packages cost less than 163p to send? How many packages cost less than 249p to send? 50

17 15 Making comparisons Objective Compare two data sets Starter Explain to students that a recent survey found that girls spent about 13 a week and boys 1 How much do you spend and what do you spend it on? Tell them that they will be finding out how to make a comparison such as what girls spend their money on compared with what boys spend their money on. Ask students to suggest some things they buy. Main teaching Show the results of the survey on slide 1 of PowerPoint 15A. How could we present these data? Take suggestions from the students and pick up on a bar chart being suggested. Move on to slide 2 to reveal a bar chart showing the girls data. Then display slide 3, which shows the boys data. How easy is it to compare the data in these two bar charts? What would make it easier? Reveal the bar charts side by side on slide 4. Does this make it easier to make comparisons? Could it be improved more? Move further through slide 4 to display the two bar charts superimposed and then move onto the enlarged version on slide 5. Discussion points How do boys compare with girls in the way they spend money? How does your spending compare with these figures? Different comparisons are best shown in different ways. Explain to students that they will be finding out more about comparing data using multiple and composite bar charts, and comparative pie charts (Higher). Key words Comparison Multiple bar chart Composite bar chart Comparative pie charts Links 9 Bar charts 12 Pie charts ActiveTeach resources MS PowerPoint presentation 15A Making comparisons Chapter 2 game Follow up section 15 (with PowerPoint 15B), Exercise 2H and Worksheets 15A and 15B section 16 (with PowerPoint 15C), Exercise 2I and Worksheet 15C (Higher) Extra practice Worksheet 15A (answers on page 181) Sections

18 PowerPoint 15B Using bar charts to make comparisons These PowerPoint presentations are on the ActiveTeach CD-ROM PowerPoint 15C Using pie charts to make comparisons 52

19 Worksheet 15A Using multiple bar charts to make comparisons section 15 A company kept records of employee absence over a two-week period during which there was a flu epidemic. Staff are employed in either production or sales. The data collected are shown in the multiple bar chart. Absentees Sales Production Mon Tue Wed Thu Fri Mon Tue Wed Thu Fri Week 1 Week 2 e) f) g) h) On which day was the highest recorded number of people absent in sales? Write down the total number of person days lost due to absence in sales. Which office recorded the highest number of absentees over the two-week period? Which was affected by the flu epidemic first, sales or production? On how many days were there more people absent from sales than from production? Between which two days was the greatest increase in absence for sales? Between which two days was the greatest increase in absence for production? On which days were there more than 10 people absent for both sales and production? 53

20 Worksheet 15B Using composite bar charts to make comparisons section 15 The composite bar chart displays data about the methods of waste disposal in three local authorities during one particular year. Authorities are expected to send as little as possible to landfill. 100% 90% 80% 70% 60% 50% Landfill Compost Recycle 40% 30% 20% 10% 0% Birmingham City Blackpool Bournemouth Source: DEFRA Municiple Waste Management Statistics Write down the name of the authority that sent the largest proportion of waste to landfill. Write down the name of the authority that is the best at recycling. Write down the name of the authority that sent the largest proportion of waste for compost. Work out an estimate for the proportion of waste Blackpool sent for landfill. The table shows the number of medals won by the top 5 countries at the Beijing Olympic Games in Draw a composite bar chart to represent these data. Gold Silver Bronze USA China Russia Great Britain Australia

21 Worksheet 15C Higher Using comparative pie charts to make comparisons section 16 The fish landed in the UK are divided into three categories. Demersal (cod, plaice et, Pelagic (herrings, sardines et and shellfish. The table below shows the catch (1000 tonnes) for two British ports. Which type of fish was landed most at Port A? Demersal Pelagic Shellfish Port A Port B Which type of fish was landed most at Port A? Which type of fish was landed least in both ports? Draw comparative pie charts to display these data. Use a circle radius of 3 cm for Port A. The pie charts show the summer sports chosen by teenagers on a summer activity programme. Boys Girls Golf Athletics Golf Athletics Tennis Tennis Cricket Cricket Explain why the pie charts are not the same size. 81 boys took part in the activities. The radius of the pie chart for boys should be 6 cm and for girls it should be 2 cm. Estimate the number of girls represented by this pie chart. Estimate the number boys who took part in cricket. 55

22 Quick Test 2A Which diagram can be used to process raw data making it easier to spot patterns? Name two types of diagram that you can use to show how data are divided into categories. The lowest mark in the class is 2% the highest is 98% and the rest of the marks lie between these values. Suggest a suitable method of grouping the data in order to draw a frequency table. The table shows the number of boys and girls in Years 10 and 11 at a school. Year 10 Year 11 Total Boys Girls Total Copy and complete the table. A toy shop sells 23 games on Monday, 15 on Tuesday, 6 on Wednesday, 32 on Thursday and 24 on Friday. Draw a vertical line graph to show this information Mon Tue Wed Thu Fri Kitchen Hall 6. The pie chart shows the relative sizes of rooms in a one-bedroom flat. Which is the largest room? Which room is half as big as the kitchen? Bathroom Living room Bedroom 56

23 Quick Test 2B Higher Which statistical diagram allows you to show the distribution but keeps the detail of the individual items of data? The multiple bar chart shows the results of four students who have taken two tests. Percentage marks Test 1 Test Jane Ali Elsa Ivan Which student showed the most improvement in the second test? Which student had the poorest result for both tests? Copy the chart and add the results for Chas who achieved 63 on the first test and 72 on the second The composite bar chart shows the numbers of staff employed by a company in 2007 and Estimate the total number of people employed by the company in Suggest a reason why the number of manual workers has decreased while the number of clerical workers has increased Manual Clerical Management A pie chart is drawn to show the comparative profits of different branches of the same company. Branch A made 20% of the total profit. What angle should represent Branch A on the pie chart? The area of farm A is 4 times as big as the area of farm B. The land use on the farms is to be compared using comparative pie charts. The radius of the pie chart for A is 6 cm. Work out the radius for farm B

24 Chapter 2 Test Foundation The Chapter Test is available in two formats: as it appears here and exam-style write-on format on the CD-ROM in the back of this Teacher Guide. The table shows the number of lessons people required before passing their driving test Copy and complete the frequency table to show the number of lessons required to pass the test. Number of lessons Tally Frequency Write down the most common class. Draw a bar chart for these data. (8) The table shows the number of free range eggs sold by a small poultry farmer in the first six months of a year. Month Number of eggs (dozens) January 8 February 6 March 16 April 12 May 18 June 20 Choose a sensible scale and draw a pictogram to display these data. Use an ellipse as the picture. (4) 3. A survey asked how many DVDs were owned by a group of people. The data collected are shown in the stem and leaf diagram Key 1 3 means 13 Write down the number of people involved in the survey. Write down the least number of DVDs owned. Write down the most number of DVDs owned. Write down the number that occurred most often. (4) 58

25 4. A council employee carried out a survey of customer satisfaction with recycling facilities. The results are shown in the bar chart. 60 Frequency Very poor Poor Satisfactory Good Very good Write down the number of people who think the recycling facilities are good. Write down the number of people who think the recycling facilities are poor. Work out how many more people think the facilities very good than very poor. Work out an estimate of the number of people who took part in the survey. (5) 5. In Argentina 14% of the population are employed in Agriculture 29% are employed in Industry 57% are employed in Service Industries. In Romania 50% of the population are employed in Agriculture 31% are employed in Industry 19% are employed in Service Industries. Draw a composite bar chart to represent these data. Give one advantage of using this type of diagram. (4) Total 25 59

26 Chapter 2 Test Higher The Chapter Test is available in two formats: as it appears here and exam-style write-on format on the CD-ROM in the back of this Teacher Guide. Write down two advantages of using a stem and leaf diagram. A company recorded its sales of new phones each day. The data are displayed in the stem and leaf diagram. e) Key 1 4 means 14 phones sold Write down the least number of phones sold. Write down the most phones sold. Work out how many days are represented on this stem and leaf diagram. Work out how many phones were sold altogether. (8) The table shows the number of TV sets in households in one street Design a cumulative frequency table for these data. Draw a cumulative frequency step polygon for these data. (6) 3. The table shows information about train times for trains from Birmingham to Preston. Birmingham Wolverhampton Stafford Crewe Warrington Wigan Preston e) f) Write down the time the from Birmingham gets into Crewe. Write down the time the from Stafford gets into Preston. Work out which of the three trains does the journey from Birmingham to Preston in the least time. There is a gap in the timetable. Explain what this means. Work out how long the takes to get from Birmingham to Stafford. Work out how long the takes to get from Crewe to Preston. (8) 60

27 4. 5. A careers convention was held in a large hotel. The 300 people attending were teachers, employers and students. 96 students attended the convention. Of these, 43 travelled by train, 26 by bus and the rest travelled by car. Out of the 140 people who travelled by train, 40 were employers. 72 people arrived in cars, of which 24 were teachers. Only 12 employers travelled by bus. Draw a table to show this information. Which form of transport was most popular with teachers? The pie chart shows the expenditure for a small company with an annual budget of 900 for office supplies. Telephone Other Stationery (5) Postage Photocopying Estimate how much was spent on stationery. Estimate how much was spent on postage. They drew this pie chart with a radius of 3 cm. The following year the company expands and the budget for office supplies is increased to What radius of pie chart should be used to display the new budget? (5) Total 32 61